A (2+1)-dimensional variable-coefficients extension of the Date-Jimbo-Kashiwara-Miwa equation: Lie symmetry analysis, optimal system and exact solutions

Article Optics

Optical solitons and conservation laws of Kudryashov's equation with improved modified extended tanh-function

Ahmed H. Arnous et al.

Summary: This paper investigates soliton solutions to Kudryashov's equation using an improved approach, presenting bright, dark, and singular optical soliton solutions. The conserved quantities are also demonstrated.

OPTIK (2021)

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Article Mathematics, Interdisciplinary Applications

Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation

Sachin Kumar et al.

Summary: The article introduces a method to obtain more exact solutions of the (4+1)-dimensional Fokas equation using the Lie group of transformation. By employing the Lie symmetry method, the Fokas equation is reduced to nonlinear ordinary differential equations which produce abundant group-invariant solutions. Numerical simulations supplement the solutions with various structures such as breather-type solitons, oscillating multi-solitons, fractal dromions, lump-type solitons, and annihilation of different solitons profiles.

CHAOS SOLITONS & FRACTALS (2021)

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Article Engineering, Aerospace

Positron nonextensivity contributions on the rational solitonic, periodic, dissipative structures for MKP equation described critical plasmas

H. G. Abdelwahed et al.

Summary: New closed forms of rational, trigonometric, periodical, explosive, hyperbolic, and shock solutions have been revealed in the ionosphere plasma of Earth. By using the Riccati-Bernoulli sub-ODE process to solve the MKP equation, researchers explored the nonextensive impacts on the features of nonlinear waves in this plasma model. The obtained new potential solutions are important achievements in plasma observations and applications in the ionosphere.

ADVANCES IN SPACE RESEARCH (2021)

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Article Physics, Multidisciplinary

Lie symmetries, optimal system and group-invariant solutions of the (3+1)-dimensional generalized KP equation

Sachin Kumar et al.

Summary: By using the Lie symmetry method, abundant group-invariant solutions were constructed for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, including various dynamic wave structures such as solitons, multi-solitons, and W-shaped solitons. The physical interpretation of soliton solutions was illustrated through three-dimensional graphical numerical simulation.

CHINESE JOURNAL OF PHYSICS (2021)

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Article Mathematics, Applied

Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation

Nardjess Benoudina et al.

Summary: This study constructs interactions of two-soliton solutions and interactions of the kink with other types of solitary wave solutions of Pavlov equation through Lie symmetry analysis. It computes a group of invariant solutions and simplifies the Pavlov equation to obtain exact solutions with physically meaningful interpretations. Physical solutions are constructed and illustrated graphically, and conservation laws are obtained for the Pavlov equation using the multiplier method.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

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Article Optics

Optical solitons of Biswas-Arshed equation in birefringent fibers using improved modified extended tanh-function method

Adel Darwish et al.

Summary: This paper addresses optical solitons in birefringent optical fibers using the Biswas-Arshed equation and the improved extended tanh-function method. Various types of traveling wave solutions are obtained, including dark, bright, and singular solitons. Graphs are presented for physical illustration of the solutions.

OPTIK (2021)

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Article Materials Science, Multidisciplinary

Novel multiple soliton solutions for some nonlinear PDEs via multiple method

Kottakkaran Sooppy Nisar et al.

Summary: In this work, analytic solutions for various types of nonlinear partial differential equations are obtained using the multiple Exp-function method. The solutions include multiple classes of soliton solutions and have been computed using the software package Maple. The obtained solutions exhibit the effects of nonlinearity and are applicable in fluid dynamics and other nonlinear phenomena.

RESULTS IN PHYSICS (2021)

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Article Mathematics, Applied

Backlund transformation and localized nonlinear wave solutions of the nonlocal defocusing coupled nonlinear Schrodinger equation

Yunqing Yang et al.

Summary: Investigation of a nonlocal integrable defocusing coupled nonlinear Schrodinger system from a 3x3 spectral problem is presented in this paper. The Backlund transformation of the nonlocal defocusing coupled nonlinear Schrodinger system is derived from pseudopotentials obtained from the Lax pair. Nonsingular localized wave solutions, including breather wave and exponential-rational solutions, are obtained and their evolutions and dynamical properties are discussed.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

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Editorial Material Physics, Multidisciplinary

Comment on: ``The modified extended tanh-function method for solving Burgers-type equations'' [Physica A 361 (2006) 394-404]

Xiangfan Piao et al.

Summary: In this letter, we analyze Soliman's paper from 2006 where he used the METF method to find exact solutions for Burgers type equations. However, we discovered that these solutions do not satisfy the corresponding Burgers equations. By correcting some of Soliman's mistakes, we provide the corrected exact solutions.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2021)

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Article Physics, Multidisciplinary

Breather solutions of the nonlocal nonlinear self-focusing Schrodinger equation

Wei-Ping Zhong et al.

Summary: The first- and second-order breather solutions of the self-focusing nonlocal nonlinear Schrodinger equation are obtained using Hirota's bilinear method. The equation is also an example of Schrodinger equation with parity-time symmetry. By utilizing recurrence relations in the Hirota bilinear form, nth-order breather solutions on the nonzero background of the NNLS equation are obtained, and the collision, superposition, and separation of transmission modes are studied.

PHYSICS LETTERS A (2021)

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Article Mathematics, Applied

Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach

Munesh Devi et al.

Summary: Nonlinear science is a common and important natural phenomenon, leading to the formulation of nonlinear partial differential equations. These equations have become a useful tool in dealing with complex natural phenomena across various branches of science. Through methods like Lie symmetry analysis, explicit exact solutions of NLPDEs can be obtained to study wave interactions and solution properties.

APPLIED MATHEMATICS AND COMPUTATION (2021)

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Article Mathematics, Applied

Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations

Xiangpeng Xin et al.

Summary: This paper investigates for the first time the integrable nonlocal couplings of Ablowitz-Kaup-Newell-Segur (NC-AKNS) equations. With the help of symmetry reduction method, the NC-AKNS equations are constructed, showing that this method can not only construct a single nonlocal equation, but also a set of equations. The Darboux transformation method is used to study the exact solutions of these nonlocal equations, resulting in a 1-fold Darboux transformation and the construction of two types of soliton solutions.

APPLIED MATHEMATICS LETTERS (2021)

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Article Physics, Multidisciplinary

Some exact invariant solutions and dynamical structures of multiple solitons for the (2+1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients using Lie symmetry analysis

Sachin Kumar et al.

Summary: The primary focus of this study is to explore the (2 + 1) dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients using Lie symmetry technique, leading to a variety of group invariant solutions such as periodic multi-solitons, single solitons, and interactions between waves.

CHINESE JOURNAL OF PHYSICS (2021)

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Article Mathematics, Applied

Two-step MPS-MFS ghost point method for solving partial differential equations

D. L. Young et al.

Summary: This paper presents a two-step method based on the method of fundamental solutions and the method of particular solutions, aiming to improve the method's performance by setting a fictitious boundary around the domain and adjusting the centers of radial basis functions. Several procedures for determining the shape parameter are introduced, and the proposed method demonstrates high accuracy and stability in highly complex and irregular domains.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2021)

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Article Mathematics, Applied