Colliding Wave Solutions in a Symmetric Non-Metric Theory

A method is given to generate the non-linear interaction (collision) of linearly polarized gravity coupled torsion waves in a non-metric theory. Explicit examples are given in which strong mutual focussing of gravitational waves containing impulsive and shock components coupled with torsion waves does not result in a curvature singularity. However, the collision of purely torsion waves displays a curvature singularity in the region of interaction.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

Numerical Soliton and Oscillating Wave Solutions for Flierl-Petviashvili Equation in Plasmas

Numerical axisymmetric soliton and oscillating wave solutions for the Flierl-Petviashvili equation in plasmas are presented. Solution branch paradigm and examples are given. Some implications of results to ion drift wave as well as force-free field of magnetic equilibrium are briefly discussed.     

Numerical Soliton and Oscillating Wave Solutions for Flierl-Petviashvili Equation in Plasmas

Numerical axisymmetric soliton and oscillating wave solutions for the Flierl-Petviashvili equation in plasmas are presented. Solution branch paradigm and examples are given. Some implications of results to ion drift wave as well as force-free field of magnetic equilibrium are briefly discussed.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.     

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.     

Two-Flux Colliding Plane Waves in String Theory

We construct the two-flux colliding plane wave solutions in higher-dimensional gravity theory with dilaton,and two complementary fluxes. Two kinds of solutions have been obtained: Bell-Szekeres (BS) type and homogeneous type. After imposing the junction condition, we find that only the BS type solution is physically well-defined. Furthermore, we show that the future curvature singularity is always developed for our solutions.     

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp\((-\phi(\xi))\)-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and anti-Kink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.     

Two-Flux Colliding Plane Waves in String Theory

We construct the two-flux colliding plane wave solutions in higher-dimensional gravity theory with dilaton, and two complementary fluxes. Two kinds of solutions have been obtained： Bell-Szekeres （BS） type and homogeneous type. After imposing the junction condition, we find that only the BS type solution is physically well-defined. Furthermore, we show that the future curvature singularity is always developed for our solutions.     

Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*

The study on the nonlocal systems is one of the hot topics in nonlinear science. In this paper, the well-known fifth-order integrable systems including the Sawada-Kotera (SK) equation, the Kaup-Kupershmidt (KK) equation and the fifth-order Koterweg-de Vrise (FOKdV) equation are extended to a generalized two-place nonlocal form, the generalised fifth-order Alice-Bob system. The Lax integrability of two sets of Alice-Bob systems for all the SK, KK and FOKdV type systems are explicitly given via matrix Lax pairs. The $\hat{P}\hat{T}$ symmetry breaking and symmetry invariant periodic and solitary waves for one set of nonlocal SK, KK and FOKdV system are investigated via a special travelling wave solution ansatz.     

A New Integrable Hierarchy,Parametric Solutions and Traveling Wave Solutions

In this paper we give a new integrable hierarchy. In the hierarchy there are the following representatives:

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota-Satsuma KdV System

In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.     

New Non-Travelling Wave Solutions of Calogero Equation

In this paper, the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation. The equation is reduced to some (1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions can be obtained.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.     

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.     

波源和接收者在介质体内的客观运动理论

建立介质体概念并指出介质体的内部独立性和外部相关性。建立双列车模型,对波在介质体内的多普勒效应进行量化分析。建立波源和接收者在介质体内的客观运动理论。把客观运动理论应用于天文学。指出天体介质体的边缘凸透镜特性。明确时间和物理介质空间的客观性。指出相对论的错误。明确波和粒子的区别。