Nonlocal symmetry, CRE solvability and soliton–cnoidal solutions of the ($$2+1$$2+1)-dimensional modified KdV-Calogero–Bogoyavlenkskii–Schiff equation
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3449-6
Abstract: In this paper, a modified KdV-CBS equation is investigated by using the truncated Painlevé expansion and consistent Riccati expansion method, respectively. It is shown that the modified KdV-CBS equation has a nonlocal symmetry related to… read more here.
Keywords: nonlocal symmetry; expansion; soliton cnoidal; modified kdv ... See more keywords
Bäcklund transformation and CRE solvability for the negative-order modified KdV equation
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3682-z
Abstract: The residual symmetry is obtained for the negative-order modified KdV (nmKdV) equation from the truncated Painlevé expansion by using symbolic computation. The multiple residual symmetries are presented and localized by introducing auxiliary variables, and then,… read more here.
Keywords: order modified; modified kdv; equation; cklund transformation ... See more keywords
A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions
Sign Up to like & getrecommendations! Published in 2018 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2017.1367440
Abstract: Abstract A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified… read more here.
Keywords: integrable equation; modified kdv; equation; negative order ... See more keywords
Two new integrable modified KdV equations, of third-and fifth-order, with variable coefficients: multiple real and multiple complex soliton solutions
Sign Up to like & getrecommendations! Published in 2019 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2019.1631504
Abstract: ABSTRACT In this work, we develop two new integrable modified KdV equations, of third and fifth orders, with time-dependent coefficients, which can be used to describe many nonlinear phenomena in fluid dynamics and solitary waves… read more here.
Keywords: new integrable; variable coefficients; two new; kdv equations ... See more keywords
Exploration of the algebraic traveling wave solutions of a higher order model
Sign Up to like & getrecommendations! Published in 2020 at "Engineering Computations"
DOI: 10.1108/ec-07-2019-0303
Abstract: Purpose The purpose of this paper is to construct the algebraic traveling wave solutions of the (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsve (KdV-Z-K) equation, which can be usually used to express shallow water wave phenomena. Design/methodology/approach The authors… read more here.
Keywords: wave solutions; dimensional modified; algebraic traveling; modified kdv ... See more keywords
Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Mathematical Physics"
DOI: 10.1155/2020/4652126
Abstract: An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the… read more here.
Keywords: system; interaction solutions; symmetry analysis; mkdv system ... See more keywords
Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations
Sign Up to like & getrecommendations! Published in 2023 at "PLOS ONE"
DOI: 10.1371/journal.pone.0283569
Abstract: The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified… read more here.
Keywords: integro differential; modified kdv; cbs; dimensional integro ... See more keywords