Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation (Q6672045): Difference between revisions

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scientific article; zbMATH DE number 7975480

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English	Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation	scientific article; zbMATH DE number 7975480

Statements

instance of

scholarly article

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title

Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation (English)

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published in

Khayyam Journal of Mathematics

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publication date

28 January 2025

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zbMATH Keywords

bilinear neural network method

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KdV equation

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traveling wave solution

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Hirota bilinear form

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MaRDI profile type

Publication

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cites work

A generalized auxiliary equation method and its applications

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Q3994822

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Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

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A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations

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Q4395060

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Nonsingular positon and complexiton solutions for the coupled KdV system

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Topological soliton solutions for three shallow water waves models

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Exact solutions to the combined KdV and mKdV equation

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Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

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New exact solutions for the KdV equation with higher order nonlinearity by using the variational method

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An extended modified KdV equation and its Painlevé integrability

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Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method

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Dynamical behaviors of different wave structures to the Korteweg-de Vries equation with the Hirota bilinear technique

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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States

0 references

Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation

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Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation

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Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method

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Exact solutions of a KdV equation hierarchy with variable coefficients

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The exact solutions to the complex KdV equation

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Complexiton solutions to soliton equations by the Hirota method

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Identifiers

DOI

10.22034/kjm.2024.396918.2865

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6672045

@@ Property / cites work @@
+A generalized auxiliary equation method and its applications
+Normal rank
@@ Property / cites work @@
+Q3994822
@@ Property / cites work: Q3994822 / rank @@
+Normal rank
@@ Property / cites work @@
+Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials
+Normal rank
@@ Property / cites work @@
+A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
+Normal rank
@@ Property / cites work @@
+Q4395060
@@ Property / cites work: Q4395060 / rank @@
+Normal rank
@@ Property / cites work @@
+Nonsingular positon and complexiton solutions for the coupled KdV system
+Normal rank
@@ Property / cites work @@
+Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method
+Normal rank
@@ Property / cites work @@
+Topological soliton solutions for three shallow water waves models
+Normal rank
@@ Property / cites work @@
+Exact solutions to the combined KdV and mKdV equation
+Normal rank
@@ Property / cites work @@
+Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method
+Normal rank
@@ Property / cites work @@
+New exact solutions for the KdV equation with higher order nonlinearity by using the variational method
+Normal rank
@@ Property / cites work @@
+An extended modified KdV equation and its Painlevé integrability
+Normal rank
@@ Property / cites work @@
+Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
+Normal rank
@@ Property / cites work @@
+Dynamical behaviors of different wave structures to the Korteweg-de Vries equation with the Hirota bilinear technique
+Normal rank
@@ Property / cites work @@
+Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
+Normal rank
@@ Property / cites work @@
+Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation
+Normal rank
@@ Property / cites work @@
+Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation
+Normal rank
@@ Property / cites work @@
+Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method
+Normal rank
@@ Property / cites work @@
+Exact solutions of a KdV equation hierarchy with variable coefficients
+Normal rank
@@ Property / cites work @@
+The exact solutions to the complex KdV equation
@@ Property / cites work: The exact solutions to the complex KdV equation / rank @@
+Normal rank
@@ Property / cites work @@
+Complexiton solutions to soliton equations by the Hirota method
+Normal rank