Some new families of spiky solitary waves of one-dimensional higher-order K-dV equation with power law nonlinearity in plasma physics

Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

“…Due to its high degree of nonlinearity, seeking exact solutions of NPDEs and conducting specific research on certain characteristics of the solutions, such as the dynamics of solitons and dispersive effects, has always been a fundamental and challenging task [4,5]. In the past decades, there has been significant progression in the development of obtaining exact solutions, such as the inverse scattering transformation [6], Bäcklund and Darboux transformations [7,8], Lie group method [9], the Hirota bilinear method [10,11], auxiliary equation mapping method [12], direct integral method [13], Pain1evé analysis [14], dressing method [15], and bifurcation method [16,17].…”

On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation

“…In recent years, NLPDEs have gained a remarkable attention in the realm of nonlinear sciences due to its wide range usage and applications. The NLPDEs perform a great role in plasma physics, ocean engineering, optical fibers, physics, biology, quantum physics, fluid mechanics, geochemistry and many other scientific areas to explain the dynamical and physical processes (Seadawy et al 2019;Seadawy and Cheemaa 2020;Zhou 2014;Younis et al 2018;Ozkan et al 2020;Ahmad et al 2020;Arshad et al 2017b, c). In this advanced era of science and technology, the study of nonlinear phenomena has become attractive field for scientists and engineers.…”

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

“…The plethora of attention has been received to determine the incipient and closed form exact solutions of FPDEs by many researchers. The potential symbolic computer programming implements have been utilized to investigate opportune solutions to NFPDEs, namely, first integral method [3][4][5], modified simple equation schemes [6,7], dirct agebric methods and auxiliary equation techniques [8][9][10], fractional equation scheme [11][12][13][14], (G /G) -expansion scheme [15][16][17], Lie-symmetry technique [18], Seadawy and Exp function methods [19][20][21][22], tanh-coth scheme [23], generalized Kudryashov scheme [24][25][26][27][28][29] and many more [30][31][32][33][34][35][36][37][38].…”