Results 141 to 150 of about 327 (166)
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Physics Letters A, 2023
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Yu-Qi Chen +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu-Qi Chen +3 more
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HBFTrans2: A Maple Package to Construct Hirota Bilinear Form for Nonlinear Equations
Communications in Theoretical Physics, 2011An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations.
Xu-Dong Yang, Hang-Yu Ruan
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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
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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
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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
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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
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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
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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
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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 ...
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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 ...
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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.
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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.
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2018
Integrable nonlineardifferential equations are an important class of nonlinear wave equations thatadmit exact soliton of the solutions. In order to construct such equations tend to apply themethod of mathematical physics, the inverse scattering problem method (ISPM),which was discovered in 1967 by Gardner, Green, Kruskal, and Miura.
ZHASSYBAYEVA, Meruyert +1 more
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Integrable nonlineardifferential equations are an important class of nonlinear wave equations thatadmit exact soliton of the solutions. In order to construct such equations tend to apply themethod of mathematical physics, the inverse scattering problem method (ISPM),which was discovered in 1967 by Gardner, Green, Kruskal, and Miura.
ZHASSYBAYEVA, Meruyert +1 more
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Erattum to: “Hirota bilinear forms with 2-toroidal symmetry”
Physics Letters A, 2000Kenji Iohara +2 more
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