Results 31 to 40 of about 987,859 (318)

KdV-type equations linked via Baecklund transformations: remarks and perspectives

, 2018
Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations.
Carillo, Sandra
core   +1 more source

Solitary wave solutions for the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation

Journal of Ocean Engineering and Science, 2017
In this paper, we utilize the exp(−φ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation. The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear
Aly R. Seadawy, Dianchen Lu, Mostafa M.A. Khater   +2 more
doaj   +1 more source

Analytical and numerical solutions with bifurcation analysis for the nonlinear evolution equation in (2+1)-dimensions

Results in Physics, 2023
This paper is focused on the nonlinear evolution equation in (2+1)-dimensions which is found in different engineering and scientific areas. Many sets of exact soliton solutions of the nonlinear evolution equation in (2+1)-dimensions are presented via two
Khalid K. Ali, M.S. Mehanna, M.A. Shaalan, Kottakkaran Sooppy Nisar, Wedad Albalawi, Abdel-Haleem Abdel-Aty   +5 more
doaj   +1 more source

Nonlinear self-interaction of plane gravitational waves

, 2003
Recently Mendonca and Cardoso [Phys. Rev. D, vol. 66, 104009 (2002)] considered nonlinear gravitational wave packets propagating in flat space-time. They concluded that the evolution equation - to third order in amplitude - takes a similar form to what ...
Brodin, G., Cardoso, V., Marklund, M., Mendonca, J. T., Servin, M.   +4 more
core   +1 more source

Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

Complex, 2019
In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton
Baoyong Guo, Huanhe Dong, Yong Fang
semanticscholar   +1 more source

The exp(−Φ(η))-expansion method with application in the (1+1)-dimensional classical Boussinesq equations

Results in Physics, 2014
Periodic and soliton solutions are presented for the (1+1)-dimensional classical Boussinesq equation which governs the evolution of nonlinear dispersive long gravity wave traveling in two horizontal directions on shallow water of uniform depth.
Harun-Or- Roshid, Md. Azizur Rahman
doaj   +1 more source

New exact solutions for time-fractional Kaup-Kupershmidt equation using improved (G′/G)-expansion and extended (G′/G)-expansion methods

Alexandria Engineering Journal, 2020
The mathematical modeling of physical systems is generally governed by evolution equations in nonlinear form. Therefore, it is critical to obtain exact analytical solutions to these equations.
S. Sahoo, S. Saha Ray, M.A. Abdou
doaj   +1 more source

Singular standing-ring solutions of nonlinear partial differential equations

, 2009
We present a general framework for constructing singular solutions of nonlinear evolution equations that become singular on a d-dimensional sphere, where d>1. The asymptotic profile and blowup rate of these solutions are the same as those of solutions of
Bricmont, Budd, Budd, Ditkowsky, Fibich, Fibich, Fibich, Gadi Fibich, Galaktionov, Galaktionoy, Gavish, Giga, Giga, Grow, Guy Baruch, Herrero, Herrero, Herrero, Ilan, Matos, Merle, Merle, Nir Gavish, Raphael, Raphael, Ren, Sulem, Velaquez, Zaag, Zaag, Zaag   +30 more
core   +1 more source

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations [PDF]

, 2013
The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered.
Akhmediev, N., Chabchoub, A., Hoffmann, N., Onorato, M., Pelinovsky, E., Sergeeva, A., Slunyaev, A.   +6 more
core   +3 more sources

Nonlinear Evolution Equations and Analyticity. I [PDF]

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1986
We prove a theorem on abstract nonlinear evolution equations ∂_tu = F(t, u) in a Banach space, which aims at estimating certain families of Liapunov functions for the solutions. The theorem is useful in proving global analyticity (in space variables) of solutions of various partial ...
Kato, Tosio, Masuda, Kyûya
openaire   +1 more source