The motive of the study was to explore nonlinear Riemann wave equation, which describes tsunami and tidal waves in sea homogeneous stationary media. This establishes framework for analytical solutions equation using new extended direct algebraic method. As a result, soliton patterns have been successfully illustrated, with exact offered by plane solution, trigonometry mixed hyperbolic periodic solutions, shock singular trigonometric single complex solutions. Graphical visualization is...

In this paper, the main motive is to mathematical explore thin-film ferroelectric material partial differential equation which addresses Ferroelectrics, that are being examined as key materials for applications in piezoelectric, pyroelectric electrostrictive, linear, and nonlinear optical systems. Thin films used a variety of modern electrical devices because they both dielectric materials. This article appropriates fractional travelling wave transformation allowing be changed into an...

In this paper, the main motive is to mathematical explore Kuralay equation, which find applications in various fields such as ferromagnetic materials, nonlinear optics, and optical fibers. The objective of study investigate different types soliton solutions analyze integrable motion induced space curves. This article appropriates traveling wave transformation allowing partial differential equation be changed into an ordinary equation. To establish these solutions, employs new auxiliary...

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to study, no previous research has presented comparision obtained generalized soliton solutions kind with power law kernel Mittag-Leffler kernel. The equations are essential in plasma physics, offering insights into collective behavior charged particles plasmas enabling diagnostics control these complex, ionized gas systems. two distinct order...

The major motive of this study is to analyze the nonlinear integrable model which generalized Kadomtsev–Petviashvili modified equal width-Burgers equation. It can be utilized extensively a weakly non-linear restoring forces, dispersion, small damping and media with dissipation narrate long wave propagation in chemical theory. This article allocates partial differential equation by traveling waves transformation into an ordinary In order acquire analytical propagating structures, one...

<abstract><p>The study aims to explore the nonlinear Landau-Ginzburg-Higgs equation, which describes waves with long-range and weak scattering interactions between tropical tropospheres mid-latitude, as well exchange of mid-latitude Rossby equatorial waves. We use recently enhanced rising procedure extract important, applicable further general solitary wave solutions formerly stated model via complex travelling transformation. Exact obtained include a singular wave, periodic...

The solution of partial differential equations has generally been one the most-vital mathematical tools for describing physical phenomena in different scientific disciplines. previous studies performed with classical derivative on this model cannot express propagating behavior at heavy infinite tails. In order to address problem, study addressed fractional regularized long-wave Burgers problem by using two operators, Beta and M-truncated, which are capable predicting where is unable show...

Abstract This work scrutinizes the well-known nonlinear non-classical Sobolev-type wave model which addresses fluid flow via fractured rock, thermodynamics and many other fields of modern sciences. The provides a more comprehensive accurate description phenomena in wide range fields. By incorporating both nonlinearity complexities dispersive waves, these models enhance our understanding natural enable precise predictions applications various scientific engineering disciplines. Therefore,...

The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications plasma physics soliton theory, where it forecasts the wave propagation profiles. In order to obtain analytically exact solitons, model under consideration a nonlinear partial differential that turned into an ordinary by using next traveling transformation. new extended direct algebraic technique modified auxiliary method are applied get solitary As result, novel...

In the present work, we utilize a new Sardar sub-equation approach, leading to successful derivation of several exact solutions for time-fractional Kudryashov's equation, which describes propagation pulses in optical fibers. These encompass range categories, including singular, wave, bright, mixed dark-bright, and bell-shaped solutions. To effectively showcase these novel soliton solutions, utilized contour plots, three-dimensional graphs, surface plots. Through multiple graphical...

This study focuses on the variant Boussinesq equation, which is used to model waves in shallow water and electrical signals telegraph lines based tunnel diodes. The aim of this find closed-form wave solutions using extended direct algebraic method. By employing method, a range with distinct shapes, including shock, mixed-complex solitary-shock, singular,mixed-singular, mixed trigonometric, periodic, mixed-shock singular, mixed-periodic, mixed-hyperbolic solutions, are attained. To illustrate...