Results 141 to 150 of about 314 (173)
Some of the next articles are maybe not open access.
A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations
Communications in Theoretical Physics, 2009An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations with logarithmic transformations is presented. In the algorithm, the general assumption of Hirota bilinear form is successfully reduced based on the property of uniformity in rank.
Yang Xu-Dong, Ruan Hang-Yu
openaire +1 more source
Trilinear Form — An Extension of Hirota’s Bilinear Form
1991Hirota’s method has been successfully applied to the soliton equations for obtaining particular solutions, especially those describing interactions of solitons [1]. The key procedure in the method is the bilinearization of the equations through dependent variable transformation.
J. Satsuma, J. Matsukidaira, K. Kajiwara
openaire +1 more source
Nonlinear Dynamics, 2021
Interaction solutions between lump and soliton are analytical exact solutions to nonlinear partial differential equations. The explicit expressions of the interaction solutions are of value for analysis of the interacting mechanism. We analyze the one-lump-multi-stripe and one-lump-multi-soliton solutions to nonlinear partial differential equations via
Lü, Xing, Chen, Si-Jia
openaire +1 more source
Interaction solutions between lump and soliton are analytical exact solutions to nonlinear partial differential equations. The explicit expressions of the interaction solutions are of value for analysis of the interacting mechanism. We analyze the one-lump-multi-stripe and one-lump-multi-soliton solutions to nonlinear partial differential equations via
Lü, Xing, Chen, Si-Jia
openaire +1 more source
Physics of Fluids, 2023
The (2+1)-dimensional generalized Hirota–Satsuma–Ito equation describing the numerous wave dynamics in shallow waters is investigated in this study. The integrable characteristics of the aforesaid equation, such as a bilinear Bäcklund transformation and Lax pair, are revealed using the Bell polynomials method.
Shailendra Singh, S. Saha Ray
openaire +1 more source
The (2+1)-dimensional generalized Hirota–Satsuma–Ito equation describing the numerous wave dynamics in shallow waters is investigated in this study. The integrable characteristics of the aforesaid equation, such as a bilinear Bäcklund transformation and Lax pair, are revealed using the Bell polynomials method.
Shailendra Singh, S. Saha Ray
openaire +1 more source
An implementation for the algorithm of Hirota bilinear form of PDE in the Maple system
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhou, Zhen-Jiang +2 more
openaire +2 more sources
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
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
International Journal of Modern Physics A, 1995
Recently there have been several studies of a nonrelativistic elastic rod in R2 whose dynamics is governed by the modified Korteweg-de Vries (MKdV) equation. Goldstein and Petrich found the MKdV hierarchy through its dynamics [Phys. Rev. Lett. 69, 555 (1992).] In this article, we will show the physical meaning of the Hirota bilinear form along the ...
openaire +2 more sources
Recently there have been several studies of a nonrelativistic elastic rod in R2 whose dynamics is governed by the modified Korteweg-de Vries (MKdV) equation. Goldstein and Petrich found the MKdV hierarchy through its dynamics [Phys. Rev. Lett. 69, 555 (1992).] In this article, we will show the physical meaning of the Hirota bilinear form along the ...
openaire +2 more sources
Communications on Applied Nonlinear Analysis
In the physical world, many real systems are governed by nonlinear partial differential equations from fluid dynamics and plasma phyasics to shallow-water waves and oceanographic systems. There is no uniform approach for solving nonlinear partial differential equations; consequently, we consider each equation as a separate problem.
openaire +1 more source
In the physical world, many real systems are governed by nonlinear partial differential equations from fluid dynamics and plasma phyasics to shallow-water waves and oceanographic systems. There is no uniform approach for solving nonlinear partial differential equations; consequently, we consider each equation as a separate problem.
openaire +1 more source
Erattum to: “Hirota bilinear forms with 2-toroidal symmetry”
Physics Letters A, 2000Kenji Iohara +2 more
openaire +1 more source