Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

2018 ◽  
Vol 32 (14) ◽  
pp. 1850143 ◽  
Author(s):  
Jin-Jin Mao ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Graphical Analysis ◽  
Optical Solitons ◽  
Series Solutions ◽  
Hirota Equation ◽  
Power Series Solutions ◽  
Propagation Properties

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

Optical solitons, complexitons and power series solutions of a (2+1)-dimensional nonlinear Schrödinger equation

2018 ◽  
Vol 32 (28) ◽  
pp. 1850336 ◽  
Author(s):  
Wei-Qi Peng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dynamical Behavior ◽  
Nonlinear Schrodinger Equation ◽  
Series Solutions ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Power Series Solutions

In this paper, a (2+1)-dimensional generalized nonlinear Schrödinger equation is investigated, which is an important model in the field of optical fiber propagation. By employing the ansatz method, we obtain the bright soliton, dark soliton and complexiton of the equation. Some constraint conditions are also derived to ensure the existence of the solitons. Moreover, its power series solutions with the convergence analysis are also provided. Some graphical analyses of those solutions are presented in order to better understand their dynamical behavior.

scholarly journals Optical solitons to the fractional Schrödinger-Hirota equation

2019 ◽  
Vol 4 (2) ◽  
pp. 535-542 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Sibel Sehriban Atas
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Solitons ◽  
Hirota Equation ◽  
3 Dimensional ◽  
Peak Intensity ◽  
Singular Soliton

AbstractThis study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

A symmetry-preserving difference scheme and analytical solutions of a generalized higher-order beam equation

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Vector Fields ◽  
Higher Order ◽  
Beam Equation ◽  
Series Solutions ◽  
Local Conservation ◽  
Power Series Method ◽  
Potential System ◽  
Power Series Solutions ◽  
The Difference

Under investigation in this work is a generalized higher-order beam equation, which is an important physical model and describes the vibrations of a rod. By considering Lie symmetry analysis, and using the power series method, we derive the geometric vector fields, symmetry reductions, group invariant solutions and power series solutions of the equation, respectively. The convergence analysis of the power series solutions are also provided with detailed proof. Furthermore, by virtue of the multipliers, the local conservation laws of the equation are derived as well. Furthermore, an effective and direct approach is proposed to study the symmetry-preserving discretization for the equation via its potential system. Finally, the invariant difference models of the generalized beam equation are successfully constructed. Our results show that it is very useful to construct the difference models of the potential system instead of the original equation.

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