Electrostatic solitary waves (ESWs) are nonlinear, isolated electric field pulses observed in space plasmas. These waves typically propagate along the direction of the magnetic field and exhibit negligible fluctuations in the perpendicular component of the magnetic field. They were first detected in auroral plasma by the S3-3 polar-orbiting satellite (Temerin et al., 1982). Later, high-resolution electric field measurements from the Geotail spacecraft revealed that broadband electrostatic noise (BEN) consists of isolated bipolar solitary structures (Matsumoto et al., 1994). Since then, ESWs have been observed in various regions of the Earth’s magnetosphere, such as the auroral zone (Ergun et al., 1998; Pickett et al., 2004), magnetopause (Cattell et al., 2002; Graham et al., 2015; Graham et al., 2016), magnetosheath (Pickett et al., 2003; Holmes et al., 2018; Shaikh et al., 2024), bow shock (Hobara et al., 2008; Wang et al., 2014; Vasko et al., 2018; Vasko et al., 2020; Sun et al., 2022; Kamaletdinov et al., 2022), plasma sheet (Ergun et al., 2009; Tong et al., 2018; Mozer et al., 2018; Wang et al., 2022), magnetotail (Norgren et al., 2015), inner magnetosphere (Vasko et al., 2017a), dusk flank region (Arya and Kakad, 2025), and so on. As new observations continue to emerge, theoretical (Singh and Lakhina, 2001; Pickett et al., 2005; Kakad et al., 2007; Lakhina et al., 2008a; Lakhina et al., 2008b, 2009; Kakad et al., 2009; Lakhina et al., 2011a; Lakhina et al., 2011b; Olivier et al., 2015; Maharaj et al., 2015; Kakad et al., 2016; Singh et al., 2024) and simulation (Omura et al., 1996; Umeda et al., 2002; Kakad et al., 2013; Kakad et al., 2014; Lotekar et al., 2016; Kakad A. et al., 2017; Lotekar et al., 2017; Vasko et al., 2017b; Dillard et al., 2018; Lotekar et al., 2019; Kakad and Kakad, 2019) studies have been conducted to investigate their generation mechanisms. In general, monopolar (double layer), bipolar, and occasionally observed tripolar structures fall under the ESW category. In this paper, the term solitary waves refers specifically to bipolar solitary structures.

In fluid models, ESWs can be classified as ion or electron acoustic solitary waves (IASWs/EASWs), depending on the dominant driving species. EASWs exhibit phase velocities of a few thousand kilometers per second, whereas IASWs typically have phase velocities of a few hundred kilometers per second. A review article on ESWs as acoustic soliton models is provided by Lakhina et al. (2021). In kinetic models, ESWs are interpreted as ion or electron holes in phase space, depending on the polarity of the associated potential structures (Eliasson and Shukla, 2006; Aravindakshan et al., 2018a; Aravindakshan et al., 2018b, Aravindakshan et al., 2020; Aravindakshan et al., 2021; Aravindakshan et al., 2023). In space plasmas, they play a role in the acceleration, heating, energy dissipation, and trapping of charged particles (Ergun et al., 2004; Andersson and Ergun, 2012; Mozer et al., 2013; Kakad et al., 2017a; Kakad et al., 2017b; Wang et al., 2023).

ESWs are not confined to Earth’s plasma environment; they have also been observed in the Martian magnetosheath (Kakad et al., 2022; Thaller et al., 2022; Pandey et al., 2025a; Pandey et al., 2025c), the Venusian plasma environment (Malaspina et al., 2020), and Saturn’s magnetosphere (Williams et al., 2006). By studying the ambient plasma parameters, various generation mechanisms have been proposed for the ESWs (Singh et al., 2022; Rubia et al., 2023; Varghese et al., 2024a; Varghese et al., 2024b). In case of Mars, in recent studies the ESWs have been reported using the electric field data from Langmuir Probe and Waves (LPW) instrument aboard the Mars Atmosphere and Volatile Evolution (MAVEN) mission. However, ESWs on Mars have not been studied as extensively as those on Earth. The LPW instrument measures the y-component of the electric field in the spacecraft’s coordinate system (Andersson et al., 2015). Therefore, limited information is available about the propagation of ESWs. A statistical study of ESWs would provide valuable insights into their occurrence in the plasma environment of an unmagnetized planet like Mars, helping to understand their role in particle dynamics. However, manual detection of solitary waves from such a large dataset is a real challenge.

In this paper, we present a tool for identifying bipolar solitary waves from the MAVEN dataset. Previously, Kojima et al. (2000) developed a method to identify ESWs from the Geotail spacecraft dataset. They employed a bit-pattern comparison technique using two sample waveforms of ESWs with opposite polarity. They defined an ESW index that quantifies the deviation from or similarity to the sample waveforms. This process is carried out by shifting the sample waveforms in time to match the observed signals. However, since the width of ESWs in the time domain can vary, different sample waveforms with varying pulse widths are required. Hansel et al. (2021) used the Solitary Wave Detector (SWD) on NASA’s Magnetospheric Multiscale (MMS) mission to map solitary waves in the Earth’s magnetosphere, identifying 60% of all bipolar solitary waves. It is based on a pseudo-standard deviation technique. In the present paper, we use a cumulative-integration-based approach to identify solitary waves. The developed tool is rigorously tested using LPW medium-frequency electric field data from the MAVEN spacecraft, and its efficiency in detecting solitary waves is examined. The paper is organized as follows: the methodology and module sequence in the program are detailed in Sections 2, 3, respectively. The usage and requirements of the Solitary Wave Identifying Tool (SWIT) are elaborated in Section 4. The results are discussed in Section 5. Finally, the study is summarized and concluded in Section 6.

First, we present the mathematical formulation of a solitary wave and outline its key properties using cumulative integration and first-order differentiation. We examined discrepancies between the ideal and observed solitary wave structures and used this information to ensure accurate identification of solitary waves in the real data. Below, in different subsections, we describe the specific criteria employed in the program to identify solitary waves. We assume the following form for the electric potential linked to the solitary wave structure, as outlined by Kojima et al. (2000) and Krasovsky et al. (1997), ϕ x = ϕ 0 ⁡ exp − x 2 λ 2 (1) where ϕ 0 is the peak of potential at position x = 0 and λ is the distance where potential falls by 1 / e times of ϕ 0 . Spacecraft measurements provide electric field data in the time domain rather than the space domain. Therefore, on substituting x = v t in Equation 1 and using E ( x ) = − d ϕ / d x , we get E t = − 1 v d ϕ d t = 2 t ϕ 0 v λ 2 exp − v 2 t 2 λ 2 (2) where v is the magnitude of the phase velocity of the solitary wave and is assumed to be constant.

To reduce parametric dependency and focus on the behavior of the electric field as a function of time, we take v = 1 , λ = 1 , and ϕ 0 = 1 ; then Equation 2 becomes, E t = 2 t ⁡ exp − t 2 (3) Equation 3 represents the typical electric field ( E ) profile of solitary waves associated with positive or negative potential and traveling in either negative or positive x − direction. Based on this, we label the electric field profiles, where the negative half-cycle occurs first, followed by the positive half-cycle, as type-1 solitary waves. Conversely, those electric field profiles where the positive half-cycle occurs first, followed by the negative half-cycle, are labeled as type-2 solitary waves. Here, the positive and negative peaks in the solitary wave profile are termed as E + and E − , with their corresponding time instances as t + and t − , respectively.

An electric field profile of the type-1 solitary waves in the time domain is shown in Figure 1A. Its cumulative integration (CI), defined as − ∫ E ( t ) d t , is displayed in Figure 1B. It may be noted that the negative sign in CI is used to maintain analogy with the electric potential. The first-order derivative of the electric field profile, E ′ ( t ) , is shown in Figure 1C. The vertical blue dashed lines indicate the instance of t − and t + , with their midpoint ( t c ) marked by the black dashed line. The vertical red dashed lines indicate the initial ( t i ) and final ( t f ) instances, where the peak of CI decreases by 99.7%. The width of the solitary wave structure ( Δ t ) is defined as the time interval between t − and t + . Here, we list properties of the ideal form of solitary wave based on Figure 1; (i) Equal absolute values of E + and E − , (ii) Equal durations of negative and positive half cycle, d − = d + (here d − = | t i − t c | and d + = | t f − t c | ), (iii) Continuous increase in the E ( t ) from t − to t + , (iv) In CI profile, no change in sign from time t i to t f , (v) Single turning point between t − to t + in E ′ ( t ) . Here, the type-1 or type-2 categories are used only for convenience, and they do not signify the polarity of the potential structure associated with the electric field. The polarity of the potential can not be identified unless the direction of propagation of solitary waves is known. We consider all the above-listed properties of the solitary wave while setting different criteria in a MATLAB executable GUI tool named SWIT to identify solitary waves. In reality, the observed solitary wave structure does not follow its exact ideal form. Therefore, while dealing with the data, the properties mentioned above are treated as references and conditionally modified to meet the requirements. The modified conditions and their implementation in the SWIT are discussed in the next Section 3.

As an example, the type-1 solitary wave structure seen in LPW electric field data is displayed in Figure 1D with its CI in panel (E) and first-order derivative in panel (F). We mark the instances t i and t f by following the turning points in the electric field before and after the t − and t + , respectively. The turning points are the locations where the slope of the curve changes its sign. As far as the first property of the solitary wave structure is concerned, it is unlikely that in real data, we encounter | E + | = | E − | . Therefore, we define a symmetry parameter for amplitude as S a = m i n { | E + | , | E − | } / m a x { | E + | , | E − | } . Here, S a can vary between 0 and 1, and S a = 1 represents 100% symmetry in amplitudes. We set a minimum acceptable limit on S a as 0.6. If S a falls below 0.6, then the bipolar electric field pulse is not treated as solitary wave. In Figure 1D, the absolute positive and negative peaks differ by 0.17 m V / m and S a = 0.95. Hence, it satisfies the acceptance criteria for being selected as solitary wave. Similarly, achieving equal durations for the positive and negative half-cycles is an ideal scenario (i.e., property-2). We defined a symmetry parameter for solitary wave half-cycle duration as S d = m i n { d − , d + } / m a x { d − , d + } . If S d exceeds 0.6, then the bipolar pulse is selected. A threshold value of 0.6 was set after visually inspecting many burst datasets. For values greater than 0.6 (such as 0.65 or 0.70), a significant number of solitary wave structures go undetected, even though they could have been identified through visual inspection.

Next, let us discuss the solitary wave properties (iii)-(v). The solitary waves are typically observed in high-resolution electric field data. Between t − and t + , a few outliers may disrupt the continuous increase of the electric field, introducing the local irregular slope variations. These variations may not be visually apparent, but they can result in multiple turning points in E ′ ( t ) within t − and t + . To address this issue, the moving average smoothing method is employed. Ideally, one anticipates a single peak in CI associated with the solitary wave. Therefore, we also examined the turning points before and after the peak of the CI. These conditions are elaborated in the next Section 3.

This subsection describes the logical workflow of different modules in the computer program, emphasizing the significance of each step in the process. For clarity, the explanation focuses solely on type-1 solitary wave, as the logic used to detect the type-2 solitary wave is identical, differing only in sign at specific points. A flowchart illustrating the main structure of the SWIT program is presented in Figure 2. It may be noted that SWIT is developed using MATLAB software.

By integrating all the conditions mentioned above, we developed a stand-alone desktop GUI application, SWIT, using MATLAB software. The requirements and instructions for the use of SWIT are given below.

In this section, we discuss the efficiency of SWIT and some results based on the analysis of medium-frequency calibrated burst mode electric field data from MAVEN for February 2015. In the development of SWIT, we ensure high efficiency, which is needed for the automatic identifier. However, in spite of all these measures, the automatic program may detect some solitary waves, which may be either false positive or false negative. Therefore, the number of solitary waves identified by visual inspection and through automatic programs can differ. In such a scenario, one needs to check the efficiency of SWIT by comparing the number of solitary waves identified visually and through SWIT. For this purpose, we took the electric field data from 1 January 2021 as an example. It contains 2,966 individual burst datasets having durations between 62.5 and 375 ms. Each individual burst is loaded in SWIT GUI with recommended input criteria (i.e., S a = 0.6, S d = 0.6, E ± FTP = 25%, and E ± STP = 25%), and solitary wave characteristics are documented. Next, for all these individual 2,966 bursts, through visual inspection, we identified the presence or absence of solitary waves and noted the total number of solitary waves for each bursts. This analysis is summarized in the Appendix Table A1. Figure 6 represents the four different burst signals from panel (A)-(D) observed on 1 January 2021. Panels (A) and (B) represent good examples of burst illustrating a series of solitary waves. Whereas panels (C) and (D) of Figure 6 represent burst examples with no solitary waves. It may be noted that in panel (A), there is one solitary wave, which is marked with a dashed rectangle. This solitary wave was selected in visual inspection, but SWIT discarded it. This is the case of a false negative. This solitary wave was discarded by SWIT due to the presence of more than one turning point in E ′ ( t ) between t − and t + as described in Section 3.2. However, SWIT has identified major solitary wave structures. In Figure 7A, we have plotted the number of solitary waves identified by SWIT (red circle) and through visual inspection (blue asterisk) for bursts grouped in 10 bins. Here, each bin contains 296 burst datasets, except for the last one, which contains 302. The corresponding efficiency is shown in Figure 7B. One can see that for most of the bins, efficiency is above 90%. Overall, a total of 738 solitary waves have been identified by visual inspection, whereas SWIT identifies 698 solitary waves. This clearly indicates that SWIT operates with high efficiency. We defined efficiency as, ϵ = 1 − [ | N obs − N SWIT | / m a x { N obs , N SWIT } ] . The efficiency, ϵ can vary between 0–1, where 1 indicates 100% efficiency. For 1 January 2021, the average efficiency is ⟨ ϵ ⟩ = 0.94.

To justify the choice of parameters S a , S d , and the turning points threshold, we considered S a and S d values of 0.55, 0.60, and 0.65, and turning points thresholds of 22.5%, 25.0%, and 27.5%. (see Table 1). Efficiency was estimated by comparing solitary waves identified through (i) visual inspection and (ii) SWIT. This analysis was performed for burst events on 1 January 2021. The efficiency was found to be highest when S a and S d were set to 0.60, and the turning points threshold to 25%. A confusion matrix corresponding to these optimal values is provided in the Appendix (see Table A2).

Further, to test SWIT, we analyzed the electric field burst datasets for 19 days in February 2015. A total of 50,835 bursts were recorded during February 2015. SWIT identified a total of 3,682 solitary waves. The mean amplitude and width of these waves are approximately 3.2 mV/m and 0.328 ms, respectively (see Table A3). The amplitude as a function of width is shown in Figure 7C for these identified solitary waves. It may be noted that, in general, the amplitude varies between ∼ 0.5 − 60 mV/m, and the durations vary between ∼ 0.5 − 1.5 ms for the considered datasets. The number of solitary waves identified in a given signal through visual inspection can vary with individual users. This variability arises because many solitary waves observed may deviate from their ideal form (refer to Figure 1). While building a SWIT, we have defined a series of criteria for identifying solitary waves. If any criterion is nearly satisfied but not fully met, the program rejects the waveform to identify it as a solitary wave. For instance, we impose a condition requiring up to 40% deviation between E max and E min . If the symmetry is 59.9%, the program will reject the solitary wave waveform. However, a user may not visually recognize the difference between 60% and 59.9% deviation. This scenario can slightly affect the detection of solitary waves. Nonetheless, these criteria are essential to minimize the identification of false positives. Sometimes, a solitary wave is embedded within random oscillations. While such a solitary wave may not be considered significant during visual inspection, SWIT can identify it if all the defined conditions are met.

The paper presents a new automatic tool to identify bipolar solitary waves from high-resolution electric field measurements by a spacecraft. It is named as SWIT and is well tested for the medium-frequency (100 Hz–32 kHz) calibrated burst mode electric field data recorded by MAVEN spacecraft. We began by discussing features of the ideal form of the solitary waves and then compared them with the observed electric field bipolar pulse. Accordingly, the criteria to identify solitary waves in the electric field data were built. The series of implemented criteria and their significance in the logical development of the computer program are elaborated. Fundamentally, SWIT is based on the cumulative integration of filtered electric field signals to identify the locations of the bipolar structures present in the data. In the output, SWIT provide E + and E − of solitary waves, with their time of occurrence t + and t − , type (i.e., type-1 or type-2) and width (in milliseconds). Additionally, the Figure visible in GUI can be exported in . f i g , . j p e g , . p n g , . e p s , . t i f , and . p d f formats. SWIT is optimized for scalability with medium-frequency burst mode electric field data. The burst durations are in multiples of 62.5 ms and could go up to 437.5 ms. The efficiency of SWIT is tested with the medium frequency electric field data recorded by MAVEN, which is found to be above 90%. While SWIT effectively identifies bipolar solitary waves, their interpretation as phase space holes or acoustic solitons is beyond the scope of the present work. Additionally, it should be noted that MAVEN measures only a single component of the electric field, which can limit the detection of solitary waves depending on the angle between the wave propagation direction and the orientation of the probes, i.e., the y-axis of the spacecraft coordinate system.

The SWIT GUI is developed using MATLAB 2024b as a stand-alone desktop application for Windows. In order to run this application, users need the MATLAB Runtime, which is included in the installer. The instructions for the installation and usage of SWIT can be found in the accompanying ReadMe file. Initially, using “process_burst_events.m” program file for MATLAB, the user can convert electric field raw data into individual “.mat” files that contain the electric field and time information separately for each burst files that occurred on a given day. These individual burst files (time and electric field) serve as input to the SWIT module. The recommended parameters for S a , S d , E ± FTP and E ± STP are 0.6, 0.6, 25% and 25%, respectively. However, the user can change these parameters. When S a and S d are increased and/or E ± FTP and E ± STP are decreased, then the conditions tend towards the ideal solitary wave.

SWIT serves as an important resource for conducting detailed statistical analyses, enabling users to explore the characteristics of solitary waves and their relationships with altitude, local time, and space weather conditions, particularly for the Martian plasma environment. The insights gained from this analysis help in understanding the generation of solitary waves in the plasma environment of unmagnetized planets like Mars. This automatic tool will reduce analysis time and aid in processing large-scale, high-resolution data acquired by spacecraft. SWIT is a versatile package that allows modifications in its code to make it applicable for high-resolution electric field datasets from other spacecraft, enabling comparative studies of solitary waves across different planetary plasma environments. In a nutshell, SWIT will be useful to explore the dynamics of bipolar solitary wave structures with good accuracy and efficiency in planetary plasma environments.