Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations
RF Zhang, MC Li - Nonlinear Dynamics, 2022 - Springer
In this work, bilinear residual network method is proposed to solve nonlinear evolution
equations. The activation function in final layer of deep neural network cannot interact with …
equations. The activation function in final layer of deep neural network cannot interact with …
Application of new Kudryashov method to various nonlinear partial differential equations
The purpose of this work is to seek various innovative exact solutions using the new
Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This …
Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This …
Bilinear auto-Bäcklund transformations and soliton solutions of a (3+ 1)-dimensional generalized nonlinear evolution equation for the shallow water waves
Y Shen, B Tian - Applied Mathematics Letters, 2021 - Elsevier
Waves are seen in the atmosphere, oceans, etc. As one of the most common natural
phenomena, water waves attract the attention of researchers. For the shallow water waves, a …
phenomena, water waves attract the attention of researchers. For the shallow water waves, a …
Rogue wave solutions and the bright and dark solitons of the (3+ 1)-dimensional Jimbo–Miwa equation
It is well known that most classical test functions to solve nonlinear partial differential
equations can be constructed via single hidden layer neural network model by using …
equations can be constructed via single hidden layer neural network model by using …
Bright-dark solitons and interaction phenomenon for p-gBKP equation by using bilinear neural network method
In the present paper, we focus on the bright-dark solitons and interaction behavior
associated with a dimensionally reduced p-gBKP equation. New test functions are …
associated with a dimensionally reduced p-gBKP equation. New test functions are …
Optical soliton solutions of variable coefficient Biswas–Milovic (BM) model comprising Kerr law and damping effect
L Kaur, AM Wazwaz - Optik, 2022 - Elsevier
This course of research is dedicated to Biswas–Milovic (BM) model with variable coefficients
comprising Kerr law and damping effect. More precisely, Biswas–Milovic (BM) equation is …
comprising Kerr law and damping effect. More precisely, Biswas–Milovic (BM) equation is …
The integrable Boussinesq equation and it's breather, lump and soliton solutions
The fourth-order nonlinear Boussinesq water wave equation, which explains the
propagation of long waves in shallow water, is explored in this article. We used the Lie …
propagation of long waves in shallow water, is explored in this article. We used the Lie …
Lump and hybrid solutions for a (3+ 1)-dimensional Boussinesq-type equation for the gravity waves over a water surface
CH Feng, B Tian, DY Yang, XT Gao - Chinese Journal of Physics, 2023 - Elsevier
In this paper, we investigate a (3+ 1)-dimensional Boussinesq-type equation, which can
elucidate the gravity waves over a water surface:(1) Via the long-wave limit method, the M th …
elucidate the gravity waves over a water surface:(1) Via the long-wave limit method, the M th …
Study on extensions of (modified) Korteweg–de Vries equations: Painlevé integrability and multiple soliton solutions in fluid mediums
This work develops two higher-dimensional extensions for both Korteweg–de Vries (KdV)
and modified KdV (mKdV) equations. We investigate the Painlevé integrability of each …
and modified KdV (mKdV) equations. We investigate the Painlevé integrability of each …
Lie symmetry reductions and group invariant solutions of (2+ 1)-dimensional modified Veronese web equation
The Lie symmetry method is successfully applied to compute group invariant solutions for
(2+ 1)-dimensional modified Veronese web equation. The purpose of this present article is …
(2+ 1)-dimensional modified Veronese web equation. The purpose of this present article is …