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Bifurcation, Phase Portrait and Traveling Wave Solutions of the Coupled Fractional Lakshmanan–Porsezian–Daniel Equation
In this paper, we investigate the bifurcation, phase portrait and the traveling wave solutions of the coupled fractional Lakshmanan–Porsezian–Daniel...
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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method
The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In...
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New Family of Solitary Wave Solutions to New Generalized Bogoyavlensky–Konopelchenko Equation in Fluid Mechanics
Many mathematicians and physicists are interested in Bogoyavlensky–Konopelchenko type equations to illustrate the various dynamics of nonlinear wave...
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Dynamical Behavior and Wave Speed Perturbations in the (2 + 1) pKP Equation
The unidirectional propagation of long waves in certain nonlinear dispersive waves is explained by the (2 + 1) pKP equation, this equation admits...
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Ground States for DNLS Equation with Periodic or Asymptotically Periodic Potential
We study the existence of ground state solutions for a class of discrete nonlinear Schrödinger equation with a sign-changing potential which is...
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Explicit Solutions of the Nonlinear Schrödinger-Type Equation
In this work, we focus on the construction of explicit solutions of the nonlinear Schrödinger-type equation, which has various applications in...
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Pre-Training Physics-Informed Neural Network with Mixed Sampling and Its Application in High-Dimensional Systems
Recently, the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential...
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A Meshless Runge–Kutta Method for Some Nonlinear PDEs Arising in Physics
This paper deals with the numerical solutions of a general class of one-dimensional nonlinear partial differential equations (PDEs) arising in...
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Investigation for Optical Soliton Solutions of Two Nonlinear Schrödinger Equations via Two Concrete Finite Series Methods
This article investigates the two cubic nonlinear Schrödinger equations which point out the evolution of disturbances in dynamics. These are
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Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation
This paper mainly introduces the parallel physics-informed neural networks (PPINNs) method with regularization strategies to solve the data-driven...
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A novel fractional case study of nonlinear dynamics via analytical approach
The present work describes the fractional view analysis of Newell-Whitehead-Segal equations, using an innovative technique. The work is carried with...
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On Lump, Periodic and Travelling Wave Structures to the Generalized Breaking Soliton Model
In this article, the generalized breaking soliton equation is considered which demonstrates the intersections of the surface wave dispersion curve...
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Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits
In this work, we study the dynamics of an infinite array of nonlinear dimer oscillators which are linearly coupled as in the classical model of Su,...
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Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity
The bifurcations and monotonicity of the period function of the Lakshmanan–Porsezian–Daniel equation with Kerr law of nonlinearity are discussed....
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Solitary wave collisions for the Whitham equation
In this article, we numerically study overtaking collisions of two solitary waves for the Whitham equation. We find regimes in which solitary wave...
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix...
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An Investigation of the Influence of Time Evolution on the Solution Structure Using Hyperbolic Trigonometric Function Methods
In attempting to mathematically create traveling wave solutions to the (2+1)-dimensional integro-differential Jaulent–Miodek equation, the extended...
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Riemann–Hilbert Approach and Multiple Arbitrary-Order Pole Solutions for the Lakshmanan–Porsezian–Daniel Equation with Finite Density Initial Data
In this work, the Riemann–Hilbert (RH) problem is employed to study the Lakshmanan–Porsezian–Daniel (LPD) equation with arbitrary-order pole points...
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Construction of the Soliton Solutions for the Manakov System by Extended Simplest Equation Method
In this paper, by using the extended simplest equation method, we study the Manakov system. Beside bright, dark and singular solitons, periodic...
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The Sasa-Satsuma Equation on a Non-Zero Background: The Inverse Scattering Transform and Multi-Soliton Solutions
We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3 × 3 matrix spectrum problem and a nonzero boundary...