The study of complexitons and periodic solitary-wave solutions with fifth-order KdV equation in (2+1) dimensions

Abstract

In this paper, the generalized fifth-order (2[Formula: see text]+[Formula: see text]1)-dimensional KdV equation is scrutinized via the extended homoclinic test technique (EHTT) and extended transformed rational function (ETRF) method. With the aid of Hirota’s bilinear form, various exact solutions comprising, periodic solitary-wave, kinky-periodic solitary-wave, periodic soliton and complexiton solutions are constructed. Moreover, the mechanical features and dynamic characteristics of the obtained solutions are presented by three-dimensional plots.

Novel nonlinear wave transitions and interactions for (2+1)-dimensional generalized fifth-order KdV equation

“…[16], the complexitons and periodic soliton solutions were also studied in Ref. [17]; nonlinear superposition phenomena between lump solitons and other forms of nonlinear localized waves were examined in Ref. [18] and the lump-periodic, breather and two-soliton solutions were presented in Ref.…”

Generalized Sub-Equation Method for the (1+1)-Dimensional Resonant Nonlinear Schrodinger’s Equation

“…Modelling and examining of such dynamical systems are generally done with some specific nonlinear differential equations. For instance, Korteweg-de Vries (KdV) [1] equation is best fitting equation for examining surface waves of shallow waters. On the other hand, Ginzburg-Landau equation is very useful in evaluating many concepts, such as superfluidity [2], Bose-Einstein condensation [3], strings in eld theory [4] and lasers [5], etc.…”