Travelling solitary wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order

In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.

An Improved Numerical Simulation Mode of Nonlinear Wave with Consideration of High Order Terms

SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.

Weak Solution of Generalized KdV Equation with High Order Perturbation Terms

By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.

HIGHER ORDER ASYMPTOTIC FIELDS AT THE TIP OF A SHARP V-NOTCH IN A POWER-HARDENING MATERIAL

The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notch angles β is obtained. The angulardistributions of stress for several cases are plotted. Theself-similarity behavior between the higher order terms is noticed.It is found that the terms with higher Order can be neglected for theV-notch angle β>45°.

Global searches of frozen orbits around an oblate Earth-like planet

A frozen orbit is beneficial for observation owing to its stationary apsidal line.The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J_(2) and limited high-order terms,which cannot meet the stringent demands of all missions.In this study,the gravitational field is expanded to J_(15) terms and the Hamiltonian canonical form described by the Delaunay variables is used.The zonal harmonic coefficients of the Earth are chosen as the sample.Short-periodic terms are eliminated based on the Hori-Lie transformation.An algorithm is developed to solve all equilibrium points of the Hamiltonian function.A stable frozen orbit with an argument of perigee that equals neither 90°nor 270°is first reported in this paper.The local stability and topology of the equilibrium points are obtained from their eigenvalues.The bifurcations of the equilibrium points are presented by drawing their global long-term evolution of frozen orbits and their orbital periods.The relationship between the terms of the gravitational field and number of frozen points is addressed to explain why only limited frozen orbits are found in the low-order term case.The analytical results can be applied to other Earth-like planets and asteroids.