两类非线性波动方程和局域性问题

本文定义了两类非线性波动方程。可以由非线性自作用项和“量子势” (或相当的项 )共同确定孤子形状和参数的方程称为第一类非线性波动方程。由于不存在“量子势”而无法确定孤子形状和参数的非线性波动方程称为第二类非线性波动方程。

一类带耗散项非线性波动问题的研究

对一类带耗散项非线性波动方程进行了研究，用“参数微分法”，得到其解析近似解。其结果可用于研讨摄动对原物理问题的解的影响，类似的问题在许多动力学问题物理解的数值定性分析及应用WKB方处理时也会常遇到。

带色散项非线性波动问题的近似解

对带色散项非线性控制方程进行了研究，用“参数微分法”，得到其近似解。结果表明，这一方法可望用于更为复杂性的非线性波动问题的理论及应用研究。

On the Blowing-up Behaviours for Nonlirear Wave Equations

This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.

On the Asymptotic Property of Solutions to Some Nonlinear Dissipative Wave Equations

In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.

Weak solution for a fourth-order nonlinear wave equation

The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.

Solving Nonlinear Wave Equations by Elliptic Equation

The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

Solution of Travelling Wave for Nonlinear Disturbed Long-Wave System

The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.

Approximate Noether-Type Symmetries and Conservation Laws via Partial Lagrangians for Nonlinear Wave Equation with Damping

In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.

Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.

Preliminary Group Classification for One Class of Nonlinear Wave Equations

The group classification is carried out on the nonlinear wave equation utt = f（x,u, ux）uzz ＋ g（x,u,uz） by using the preliminary group classification approach. The generators of equivalence group are determined and the corresponding reduced forms are obtained. The result of the work is shown in table form.

Solutions to a Novel Casimir Equation for the Ito System

We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.

On an Auto-Baecklund Transformation for (2+1)-Dimensional VariableCoefficient Generalized KP Equations and Exact Solutions

By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves.

Application of Seismic Inversion Using Logging Data as Constraints in Coalfield

Seismic inversion and basic theory are briefly presented and the main idea of this method is introduced. Both non-linear wave equation inversion technique and Complete Utilization of Samples Information (CUSI) neural network analysis are used in lithological interpretation in Jibei coal field. The prediction results indicate that this method can provide reliable data for thin coal exploitation and promising area evaluation.

Financial Rogue Waves

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.

Modelling of ultrasonic motor with dead-zone based on Hammerstein model structure

The ultrasonic motor (USM) possesses heavy nonlinearities which vary with driving conditions and load-dependent characteristics such as the dead-zone. In this paper, an identification method for the rotary travelling-wave type ultrasonic motor (RTWUSM) with dead-zone is proposed based on a modified Hammerstein model structure. The driving voltage contributing effect on the nonlinearities of the RTWUSM was transformed to the change of dynamic parameters against the driving voltage. The dead-zone of the RTWUSM is identified based upon the above transformation. Experiment results showed good agreement be- tween the output of the proposed model and actual measured output.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.

A Class of Singularly Perturbed Nonlinear Shock Problems

Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtained. And the known results are generalized.

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.