Closed-form solutions to the solitary wave equation in an unmagnatized dusty plasma

This paper is devoted to closed-form solutions of the partial differential equation:θxx+θyy+δexp(θ)=0, which arises in the steady state thermal explosion theory. We find simple exact solutions of the formθ(x,y)=Φ(F(x)+G(y)), andθ(x,y)=Φ(f(x+y)+g(x-y)). Also, we study the corresponding nonlinear wave equation.

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Closed-form solutions for the Schrödinger wave equation with non-solvable potentials: A perturbation approach

Open Physics ◽

10.1515/phys-2021-0028 ◽

2021 ◽

Vol 19 (1) ◽

pp. 208-214

Author(s):

Haifa Ibrahim Alrebdi ◽

Thabit Barakat

Keyword(s):

Wave Equation ◽

Closed Form ◽

Bound States ◽

Perturbation Technique ◽

Scalar Potential ◽

Asymptotic Iteration Method ◽

Perturbation Approach ◽

Closed Form Solutions ◽

Solvable Potential ◽

Unperturbed Problem

Abstract To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

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Closed-form solutions and conservation laws of a generalized Hirota–Satsuma coupled KdV system of fluid mechanics

Open Physics ◽

10.1515/phys-2021-0002 ◽

2021 ◽

Vol 19 (1) ◽

pp. 18-25

Author(s):

Chaudry Masood Khalique

Keyword(s):

Solitary Wave ◽

Fluid Mechanics ◽

Conservation Laws ◽

Exact Solutions ◽

Closed Form ◽

Solitary Wave Solutions ◽

Linear Ordinary Differential Equations ◽

Closed Form Solutions ◽

Wave Solutions ◽

Simplest Equation Method

Abstract In this article, a generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system is investigated from the group standpoint. This system represents an interplay of long waves with distinct dispersion correlations. Using Lie’s theory several symmetry reductions are performed and the system is reduced to systems of non-linear ordinary differential equations (NLODEs). Subsequently, the simplest equation method is invoked to find exact solutions of the NLODE systems, which then provides the solitary wave solutions for the system under discussion. Finally, we construct conservation laws of generalized Hirota–Satsuma coupled KdV system with the aid of general multiplier approach.

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Solutions of Generalized Fractional Perturbed Zakharov-Kuznetsov Equation Arising in a Magnetized Dusty Plasma

Revista Mexicana de Física ◽

10.31349/revmexfis.67.060703 ◽

2021 ◽

Vol 67 (6 Nov-Dec) ◽

Author(s):

Lanre Akinyemi

Keyword(s):

Solitary Wave ◽

Plasma Physics ◽

Closed Form ◽

Dusty Plasma ◽

Analytical Solutions ◽

Quantum Physics ◽

Mathematical Physics ◽

Future Research ◽

Ion Temperature ◽

Magnetized Dusty Plasma

The generalized fractional perturbed (3+1)-dimensional Zakharov–Kuznetsov (PZK) equation which appear in the magnetized two-ion-temperature dusty plasma and quantum physics is considered. The sub-equation method in the conformable sense is proposed to obtained closed-form analytical solutions to this equation. The newly solutions obtained by the proposed method are kink-shape, multi-soliton, solitary wave, bell-shaped solitons, and periodic solutions that are substantial in the field of mathematical physics and can be of relevance in the field of plasma physics, also for future research.

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