Unveiling three-dimensional sea surface signatures caused by internal solitary waves:insights from the surface water ocean topography mission

Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

Spatial and temporal variation process of seabed dynamic response induced by the internal solitary wave

Internal solitary wave(ISW)is often accompanied by huge energy transport,which will change the pore water pressure in the seabed.Based on the two-dimensional Biot consolidation theory,the excess pore water pressure in seabed was simulated,and the spatiotemporal distribution characteristics of excess pore water pressure was studied.As the parameters of both ISW and seabed can affect the excess pore water pressure,the distribution of pore water pressure showed both dissipation and phase lag.And parametric studies were done on these two phenomena.Due to influenced by the phase lag of excess pore water pressure,the penetration depth under the site of northern South China Sea with total water depth 327 m,induced by typical internal solitary wave increased by 26.19%,53.27%and 149.86%from T_(0)to T_(0.5)in sand silt,clayey silt and fine sand seabed,respectively.That means the effect of ISW on seabed will be underestimated if we only take into accout the penetration depth under ISW trough,especially for fine sand seabed.In addition,the concept of“amplitude-depth ratio”had been introduced to describe the influence of ISW on seabed dynamic response in the actual marine environment.In present study,it is negatively correlated with the excess pore water pressure,and an ISW with smaller amplitude-depth ratio can wide the range of lateral impacts.Our study results help understand the seabed damage induced by the interaction between ISW and seabed.

Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method

In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.

An Extended Riccati Equation Method to Find New Solitary Wave Solutions of the Burgers-Fisher Equation

In this paper, our objective is to explore novel solitary wave solutions of the Burgers-Fisher equation, which characterizes the interplay between diffusion and reaction phenomena. Understanding this equation is crucial for addressing challenges in fluid, chemical kinetics and population dynamics. We tackle this task by employing the Riccati equation and employing various function transformations to solve the Burgers-Fisher equation. By adopting different coefficients in the Riccati equation, we obtain a wide range of exact solutions, many of which have not been previously documented. These abundant solitary wave solutions serve as valuable tools for comprehending the Burgers-Fisher equation and contribute to expanding our knowledge in this field.

EXACT SOLITARY WAVE AND SOLITONSOLUTIONS OF THE FIFTH ORDER MODEL EQUATION

With the aid of nonlinear transformations, and using the symbolic manipulation system, the exact solitary wave and soliton solutions to a fifth order nonlinear evolution equation with general coefficients are obtained, and the corresponding sufficient conditions that the equation admits of these type of solutions are given. From the results one can see how the apparently changes in the coefficients would effect the solutions.

Exact self-similar solitary waves and collisions in nonlinear optical media

This paper analyses bright and dark spatial self-similar waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. It finds an appropriate transformation for the first time such that the nonlinear Schrodinger equation （NLSE） with varying coefficients transform into standard NLSE. It obtains one-solitonlike, two-solitonlike and multi-solitonlike self-similar wave solutions by using the transformation. Furthermore, it analyses the features of the self-similar waves and their collisions.

SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.

(2+1)-dimensional dissipation nonlinear Schrdinger equatio for envelope Rossby solitary waves and chirp effect

In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.

Solitary Wave Simulated by the Water Column Collapsing Method

Although solitary waves with large ratio of wave height to water depth are difficult to produce in laboratory settings by traditional wave generating methods,a water column collapsing(WCC)method can be employed.This study uses the WCC method to produce large solitary waves and through a series of experiments,an empirical equation is developed that considers wave height and water depth in addition to water column height and depth.Generated solitary waves are studied through wavelet transforms.Results from this analysis demonstrate that the ratios between the initial lab-oratory-generated solitary wave and its theoretical counterpart range from 0.2−0.8.By using the results,a new solitary wave generating law is derived and can be applied to future solitary wave laboratory studies.

On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations

In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper,the approximate expressions of the solitary wave solutions for a class of nonlinear disturbedlong-wave system are constructed using the homotopic mapping method.

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.

Solitary Waves for Cubic-Quintic Nonlinear Schroedinger Equation with Variable Coefficients

cubic-quintic 非线性的 Schrodinger 方程(CQNLS ) 在光纤维和原子水动力学起重要作用。由为 cubic-quintic 使用同类的平衡原则，钟类型，纽结类型，代数学的独居的波浪，和三角法的旅行波浪，有可变系数(vCQNLS ) 的非线性的 Schrodinger 方程在一套辅助高顺序的平常的微分方程的帮助下被导出(亚方程为短) 。在这篇论文使用的方法可能帮助一个为 otherhigh 顺序导出准确答案非线性的进化方程，和表演同类的平衡原则的新申请。

Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation

With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions,four types of exact solutions of the generalized derivative nonlinear Schrdinger equation (GDNLSE) have been foundout,which are the bell-type solitary wave solution,the algebraic solitary wave solution,the kink-type solitary wavesolution and the sinusoidal traveling wave solution,provided that the coefficients of GDNLSE satisfy certain constraintconditions.For more general GDNLSE,the similar results are also given.

Grey Self-similar Solitary Waves in Inhomogeneous Nonlinear Media

这篇论文在等级索引分析空间灰自我类似的独居的波浪繁殖和碰撞有自我集中、自我散焦的克尔非线性的非线性的波导放大器。新准确自我类似的答案用新奇转变被发现，他们的主要特征被使用直接计算机模拟调查。

Nonpropagating Solitary Waves in （2＋1）-Dimensional Nonlinear Systems

By means of extended homogeneous balance method and variable separation approach, quite a general variable separation solution of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation is derived. From the variable separation solution and by selecting appropriate functions, a new class of (2+1)-dimensional nonpropagating solitary waves are found. The novel features exhibited by these new structures are first revealed.