Results 91 to 100 of about 697 (208)

Advanced Mathematical Approaches for the Kadomtsev–Petviashvili and Bogoyavlensky–Konopelchenko Equations in Applied Sciences

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
The Kadomtsev–Petviashvili (KP) equation and the Bogoyavlensky–Konopelchenko (BK) equation are fundamental models in the study of nonlinear wave dynamics, describing the evolution of weakly dispersive, quasi‐two‐dimensional (2D) wave phenomena in integrable systems.
Md. Abdul Aziz, Jingli Ren
wiley   +1 more source

Hirota bilinear forms of evolution type equations and their interaction solutions

, 2023
Bu tez çalışmasında bazı oluşum tipi denklemlerin Hirota metodu ile tam çözümlerinin elde edilmesi araştırılmıştır. Bu anlamda Hirota bilineer formuna sahip olan yeni bir (3+1)-boyutlu oluşum tipi modelin çeşitli fiziksel özellikleri haiz olan tam ...
Zeynel, Melih
core   +1 more source

Two-mode coupled Burgers equation: Multiple-kink solutions and other exact solutions

Alexandria Engineering Journal, 2018
In this paper, we establish a new two-mode coupled Burgers equation (TMCBE). The necessary conditions that make the multiple kink solutions and the multiple singular kink solutions to TMCBE exist are founded using the simplified bilinear method. Moreover,
H.M. Jaradat
doaj   +1 more source

Bilinear approach to soliton and periodic wave solutions of two nonlinear evolution equations of Mathematical Physics

Advances in Difference Equations, 2019
In the present paper, the potential Kadomtsev–Petviashvili equation and ( 3+1 $3+1$)-dimensional potential-YTSF equation are investigated, which can be used to describe many mathematical and physical backgrounds, e.g., fluid dynamics and communications ...
Rui Cao, Qiulan Zhao, Lin Gao
doaj   +1 more source

Solving bi-directional soliton equations in the KP hierarchy by gauge transformation [PDF]

, 2006
We present a systematic way to construct solutions of the (n = 5)-reduction of the BKP and CKP hierarchies from the general τ function τn+k of the KP hierarchy.
Cheng, Yi, He, Jingsong, He, J.S., Roemer, Rudolf A., Cheng, Y.   +4 more
core   +1 more source

Elastic and resonant interactions of a lump wave and solitary waves for the (2+1)-dimensional Ito equation

Results in Physics
In this paper, by using of a transformation with a parameter, together with the Hirota bilinear method, we obtain the 3-solitary wave and 4-solitary wave solutions of the (2+1)-dimensional Ito equation.
Meng-Yao Wang, Ai-Hua Chen, Lun-Jie Zhang   +2 more
doaj   +1 more source

Analyzing Soliton Solutions of the (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: Comprehensive study of dark, bright, and periodic dynamics

Results in Physics
This paper investigates the (n+1) dimensional integrable extension of the Kadomtsev–Petviashvili (KP) equation. The study focuses on extracting Auto-Bäcklund transformations for the given model using the extended homogeneous balance (HB) method in ...
Nauman Raza, Ahmed Deifalla, Beenish Rani, Nehad Ali Shah, Adham E. Ragab   +4 more
doaj   +1 more source

Hirota-sato formalism via maya diagrams on KP, KdV and S-K equations [PDF]

, 2012
This article illustrates Hirota-Sato formalism by establishing that Hirota’s direct method is derivable from Sato theory. This formalism is considered via Maya diagrams and used to describe the Kadomtsev-Petviashvili (KP), Korteweg-de Vries (KdV) and ...
Abdul Aziz, Zainal, Ali, Noor Aslinda
core  

N-soliton solutions for the (2+1)-dimensional Hirota–Maccari equation in fluids, plasmas and optical fibers

, 2011
Under investigation in this paper is the Hirota–Maccari equation, which is a generalized (2+1)-dimensional model in fluid dynamics, plasma physics and optical fiber communication.
Yu, Xin, Ming-Zhen Wang, Ying Liu, Feng, Qian, Yi-Tian Gao, Qian Feng, Zhi-Yuan Sun, Gao, Yi-Tian, Liu, Ying, Sun, Zhi-Yuan, Wang, Ming-Zhen, Xin Yu, Meng, Xiang-Hua, Xiang-Hua Meng   +13 more
core   +1 more source

Application of Hirota's Direct Method to Nonlinear Partial Differential Equations: Bilinear Form and Soliton Solutions

, 2022
The Hirota method to get the soliton solutions for a nonlinear partial differential equation is the mostefficient direct technique researchers use worldwide. This article reviews and explores Hirota’s directtechnique on the KdV equation, which Hirota initially used to clarify his method.
openaire   +1 more source