Open AccessTraveling wave solutions for the extended modified KORTEWEG-DE VRIES equation
Author(s) -
Gaukhar Shaikhova,
AUTHOR_ID,
Berik Rakhimzhanov,
AUTHOR_ID
Publication year - 2021
Publication title -
vestnik nacionalʹnoj inženernoj akademii respubliki kazahstan
Language(s) - English
Resource type - Journals
eISSN - 2709-4707
pISSN - 2709-4693
DOI - 10.47533/2020.1606-146x.130
Subject(s) - korteweg–de vries equation , dispersionless equation , integrable system , sine gordon equation , mathematics , partial differential equation , soliton , nonlinear system , mathematical analysis , mathematical physics , trigonometric functions , traveling wave , kadomtsev–petviashvili equation , differential equation , physics , burgers' equation , quantum mechanics , geometry
In this paper, we study an extended modified Korteweg-de Vries equation, which contains the relevant higher-order nonlinear terms and fifth-order dispersion. This equation is the extension of the modified Korteweg-de Vries equation and described by the Ablowitz-Kaup-Newell-Segur hierarchy. The standard Korteweg-de Vries equation is the pioneer integrable model in solitary waves theory, which gives rise to multiple soliton solutions. The Korteweg-de Vries equation arises naturally from shallow water, plasma physics, and other fields of science. To obtain exact solutions the sine-cosine method is applied. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics. Traveling wave solutions are determined for extended modified Korteweg-de Vries equation. The study shows that the sine–cosine method is quite efficient and practically well suited for use in calculating traveling wave solutions for extended modified Korteweg-de Vries equation.