Optical soliton solutions, explicit power series solutions and linear stability analysis of the quintic derivative nonlinear Schrödinger equation

2019 ◽  
Vol 51 (3) ◽  
Author(s):  
Wenhao Liu ◽  
Yufeng Zhang
Keyword(s):  
Stability Analysis ◽  
Power Series ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Series Solutions ◽  
Power Series Solutions ◽  
Derivative Nonlinear Schrödinger Equation

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.

Finite Element Formulation for Linear Stability Analysis of Axially Functionally Graded Nonprismatic Timoshenko Beam

2019 ◽  
Vol 19 (02) ◽  
pp. 1950002 ◽  
Author(s):  
Masoumeh Soltani ◽  
Behrouz Asgarian
Keyword(s):  
Stability Analysis ◽  
Power Series ◽  
Linear Stability ◽  
Timoshenko Beam ◽  
Linear Stability Analysis ◽  
Functionally Graded ◽  
Element Formulation ◽  
Variable Cross ◽  
Timoshenko Beams ◽  
Stiffness Matrices

An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Timoshenko beam theory, the equilibrium equations are derived in the context of small displacements, considering the coupling between the transverse deflection and angle of rotation. The system of stability equations is then converted into a single homogeneous differential equation in terms of bending rotation for the cantilever, which is solved numerically with the help of the power series approximation. All the mechanical properties and displacement components are thus expanded in terms of the power series of a known degree. Afterwards, the shape functions are gained by altering the deformation shape of the AFG nonprismatic Timoshenko beam in a power series form. At the end, the elastic and buckling stiffness matrices are exactly determined by the weak form of the governing equation. The precision and competency of the present procedure in stability analysis are assessed through several numerical examples of axially nonhomogeneous and homogeneous Timoshenko beams with clamped-free ends. Comparison is also made with results obtained using ANSYS and other solutions available, which indicates the correctness of the present method.

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.

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.

MODULATIONAL INSTABILITY OF DIPOLAR BOSE–EINSTEIN CONDENSATES IN AN OPTICAL LATTICE

2010 ◽  
Vol 24 (29) ◽  
pp. 5695-5701 ◽  
Author(s):  
HAIFENG CHEN ◽  
JINSONG HUANG ◽  
ZHENGWEI XIE
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Optical Lattice ◽  
Schrodinger Equation ◽  
Modulational Instability ◽  
Great Influence ◽  
Nonlinear Schrodinger Equation ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Bose Einstein

From the discrete nonlinear Schrödinger equation and the linear stability analysis, the modulational instability (MI) of dipolar Bose–Einstein Condensates (BECs) in an optical lattice is studied. The MI relation of the dipolar BECs in the optical lattice with the on-site interaction and the inter-site interaction is obtained. The results show that there is a great influence of inter-site interaction on MI of dipolar BEC in the optical lattice. This gives us some useful information for manipulating dipolar BECs in practice.

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