Results 91 to 100 of about 468 (168)

Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams [PDF]

, 2013
This work relates Hirota direct method to Sato theory. The bilinear direct method was introduced by Hirota to obtain exact solutions for nonlinear evolution equations.
Ali, Noor Aslinda
core  

Dissipative hierarchies and resonance solitons for KP-II and MKP-II

, 2007
We show that dissipative solitons (dissipatons) of the second and the third members of SL(2,R) AKNS hierarchy give rise to the real solitons of KP-II, while for SL(2,R) Kaup-Newell hierarchy they give solitons of MKP-II.
Pashaev, Oktay, Lee, Jyh Hao, Francisco, Meltem L. Y.   +2 more
core   +1 more source

The Hirota's direct method and multi-soliton solutions [PDF]

, 2010
The study of soliton theory is always a major source of mathematical and physical inspiration. For the past few decades, soliton theory has attracted considerable attention in diverse physical applications and the various mathematical methods of solution.
Chia, Chee Pen
core  

Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach

Results in Physics
This manuscript addresses the rational solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, emphasizing key aspects in response to specific questions.
Mati ur Rahman, Mohammad Alqudah, Meraj Ali Khan, Bent Elmina Haroun Ali, Shabir Ahmad, Emad E. Mahmoud, Mei Sun   +6 more
doaj   +1 more source

Propagation of dark solitons with higher-order effects in optical fibers

, 2001
In this paper, we analyze dark soliton propagation in nonlinear optical fibers with higher-order effects such as third order dispersion, self-steepening, and stimulated Raman scattering.
Mahalingam, A., Porsezian, K.
core   +1 more source

Chaotic behaviour, bifurcation, and stability analysis of the time-fractional phi-four model using the Hirota bilinear form

This study investigates the complex dynamics of the time-fractional Phi-four model, a nonlinear PDE that incorporates memory effects through fractional derivatives.
Al Mamun, Abdulla, Ananna, Samsun Nahar, Amin Meia, Md Al, Lu, Chunhui   +3 more
core   +1 more source

Multi-Soliton solutions to a model equation for shallow water waves

, 2010
In Soliton theory, Hirota direct method is most efficient tool for seeking one soliton solutions or multi-soliton solutions of integrable nonlinear partial differential equations.
Qiao, Zhijiang
core  

Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods

, 2017
This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.
Wiggins, Benjamin
core  

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions. [PDF]

Heliyon, 2023
Guo B, Fang Y, Dong H.
europepmc   +1 more source

Exact soliton, lump, and breather solutions of the (3 + 1)-dimensional Jimbo-Miwa equation via the bilinear neural network method. [PDF]

Sci Rep
Hussein HH, Mekawey H, Elsheikh A.
europepmc   +1 more source