Conservation laws and new exact solutions to the maccari’s modulation equations

Ghosh, Arindam; Maitra, Subhamoy

doi:10.1088/1402-4896/acba57

Cited by 3 publications

(1 citation statement)

References 46 publications

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“…The reproducing kernel Hilbert space method (RKHSM) is used by Attia and Akgul [48] to efficiently solve nonlinear PDEs that arise in acoustic issues for fluid flow. Ghosh and Maitra [49] discuss and use an efficient algorithmic technique called the multiplier approach to find the conservation laws for the Maccari system. The (3+1)-dimensional variable coefficient is addressed by Singh and Ray [50].…”

Section: Introductionmentioning

confidence: 99%

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

Jena,

Sahu

2023

Phys. Scr.

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In this paper we investigate approximate analytical solution so called voltage in one and two space variables for linear and nonlinear telegraph equations by a reliable method namely Modified Laplace Decomposition Method (MLDM) using MATLAB and MATHEMATICA software tools. The MLDM is a mixture of Laplace transform with modified Adomian decomposition method based on Newton Raphson method. The nonlinearity of the problem is tackled by Adomian decomposition and approximate analytical solution to the partial differential equation handled by using the Laplace and inverse Laplace transform technique without differentiation in time domain. We use Newton Raphson method in the domain of Adomian polynomial to modify it. Theoretical concepts for the approximate analytical solution of present scheme are well behaved through stability and convergence analysis. Five numerical examples are carried out in order to check the effectiveness and applicability of the proposed scheme. The telegraph equation with one space variable is solved numerically whereas the approximate analytical solution obtained for two space variables. Employing MLDM, it is possible to obtain the approximate analytical solution (i.e., voltage) of a telegraph equation and found to be in good agreement with exact solutions and also compared with earlier studies for one space variable.

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Section: Introductionmentioning

confidence: 99%

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

Jena,

Sahu

2023

Phys. Scr.

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Conservation laws, traveling wave solutions and wavelet solution for the two-component Novikov equation

Mondal,

Maitra

2024

J. Phys. A: Math. Theor.

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The objective of this present article is to study the two-component Novikov equation. This equation is also known as Geng-Xue equation and is characterized by cubic nonlinearities. By applying the multiplier method, new conserved quantities are found, and some traveling wave solutions are derived based on the (G′/G )-expansion method. Furthermore, a numerical solution is determined by employing the Haar wavelet collocation method. In order to confirm the accuracy, this numerical solution is compared with the solution obtained by (G′/G )-expansion method. Additionally, the convergence analysis of the Haar wavelet collocation method is also presented.

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Exploration of soliton structures in the Hirota–Maccari system with stability analysis

Alam,

Ma,

Ullah

et al. 2024

Mod. Phys. Lett. B

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In this research, the modified extended tanh-function (METF) and the extended Jacobi elliptic function expansion (EJEFE) techniques are used to investigate the generation and detection of soliton structures in the Hirota–Maccari (HM) model. Consequently, we obtain soliton solutions with advanced structures, including singular bright soliton, dark soliton, periodic waves, breather waves, periodic breather waves, and multiple bright and dark breather waves. In addition, a lump-type breather wave is also included in the presented solutions. Stability analysis of the obtained solutions is addressed by employing the Hamiltonian technique. 3D surfaces and 2D visuals of the outcomes are represented with the help of a computer application. These findings contribute to understanding nonlinear wave phenomena with potential applications in optics, fluid dynamics, and plasma physics.

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Conservation laws and new exact solutions to the maccari’s modulation equations

Cited by 3 publications

References 46 publications

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

Conservation laws, traveling wave solutions and wavelet solution for the two-component Novikov equation

Exploration of soliton structures in the Hirota–Maccari system with stability analysis

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