New various multisoliton kink‐type solutions of the (1 + 1)‐dimensional Mikhailov–Novikov–Wang equation

Abstract

In this article, a (1 + 1)-dimensional Mikhailov-Novikov-Wang equation is examined by using simplified Hirota's method. The kink-type multisoliton solutions are obtained successfully for the equation. The solutions obtained are displayed graphically in order to demonstrate the properties.

Field and reverse field solitons in wave-operator nonlinear Schrödinger equation with space-time reverse: Modulation instability

“…A fully discrete scheme by discretizing the space with the local discontinuous Galerkin method and the time with the Crank-Nicholson scheme to simulate the multi-dimensional Schrödinger equation with a wave operator was presented [29,30]. Some relevant works in this area were carried out [31][32][33][34][35][36][37][38][39] Here, we consider the wave-operator nonlinear Schrödinger equation with space and time reverse (W-O-NLSE-STR) and use conventional forms for its solutions in two cases; when the field and its reverse are not interactive and when they are interactive. This is done together with implementing the unified method (UM) [40][41][42][43][44][45].…”

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

“…-expansion approach and the sine-Gordon expansion method in [19]; the analytic solutions to a generalized super-NLS-mKdV equation are determined by employing the Darboux transformation technique in [20]; the solution families in the form of Jacobi elliptic function to the resonant NLS equation have been derived via a new Ф 6 -model expansion approach in [21]; modified Pfaffian technique is utilized to derive the hybrid wave solutions of shallow water wave equation in (2 + 1)-dimensions in [22] and to find the nonlinear wave solutions of generalized (3 + 1)dimensional Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in [23]; modified tanh-expansion approach is used to obtain the optical solutions of Fokas-Lenells equation in [24]; Hirota bilinear method has been utilized to derive the breather, soliton, and rogue wave solutions of cylindrical Kadomtsev-Petviashvili equation in [25]; auxiliary equation approach is utilized to derive the periodic wave solutions of fractional Dullin-Gottwald-Holm equation in [26]; simplified Hirota method has been utilized to find the bright soliton solutions of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equations in [27] and to derive the kink-type multi-soliton solutions of the Mikhailov-Novikov-Wang (MNW) equation in [28]; Painlevé analysis method is utilized to examine the integrability of MNW equation in [29]; Painlevé analysis approach along with auto-Bäcklund transformation approach is employed to find the integrability and numerous analytical solutions of variable coefficients generalized (2 + 1)-dimensional Burgers system in [30], generalized KdV6 equation with variable coefficients in [31] and modified variable coefficients KdV equation in [32].…”

Multi-soliton solutions and soliton molecules of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for the incompressible fluid

“…In eq. ( 3), D m x D n t indicates the Hirota bilinear derivative as [33,34] To get the 1-soliton solution, we can assume [35]…”

“…For the 3-soliton solution, we set [35] f = 1 + e ζ1 + e ζ2 + e ζ3 + Λ 12 e ζ1+ζ2 + Λ 13 e ζ1+ζ3 + Λ 23 e ζ2+ζ3 + Λ 123 e ζ1+ζ2+ζ3 , (…”