Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities

Abstract

In this work, we study a variety of nonlinear evolution equations with logarithmic nonlinearities. We will examine the logarithmic KdV-like equations, the logarithmic KP-like equations, and the logarithmic Klein-Gordon equations. We show that these equations possess Gaussons: solitary wave solutions of Gaussian shape.

New Optical Solitons of the Longitudinal Wave Equation in a Magnetoelectro-Elastic Circular Rod

“…Zayed and Alurrfi [22] reported the results of a research in which the modified Kudryashov method was adopted to produce a number of exact solutions for nonlinear seventh-order SawadaKotera-Ito equation, the nonlinear seventh-order KaupKupershmidt equation and the nonlinear seventh-order Lax equation. For more research papers, see [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. This paper illustrates the effectiveness of the modified Kudryashov method in finding a number of new optical solitons for the nonlinear longitudinal wave equation in * corresponding author; e-mail: qinzhou@whu.edu.cn a magnetoelectro-elastic circular rod [43] …”

Breather structures in a plasma with warm ions and Cairns electrons

“…[1][2][3][4][5] Nowadays, the investigation of the non-linear waves and their propagation characteristics in a plasma has become an important subject of plasma physics. exists in different plasma systems and non-linear medium due to the presence of various types of non-linearities.…”

Construction of a hierarchy of negative‐order integrable Burgers equations of higher orders

“…We can show that this variety of equations nicely passes a Painlevé test, which indicates typically its integrability. The Hirota's method introduced by Hirota, 14 and its simplified form that was thoroughly used in the literature in several studies, [12][13][14][15][16][17][18][19][20][21][22][23][24] will be used to obtain multiple kink solutions for some of these constructed equations, and then for the generalized negative-order Burgers equation. We expect our study to provide further development of more hierarchies of integrable equations.…”