The Solution To Some Nonlinear Models In Mechanics And Biology

Although there are mathematical models for some practical problems in in mechanicsand biology, most models need the exact solutions. We can describe various phenomena andanalyse varous images by studying the solutions to the nonlinear models and then judge andcorrect the practical problems. At present, mathematicians,physicists and biologists at homeand abroad have made great progress in solving nonlinear models, such as Hirota bilinearmethod[11], limited expansion method, Lie method[12-13], Tanh function method[14-17],homogeneous balance method[18], nonlinear transform method and so on. But these solutionshave some limitations due to the condition of computer, and they can only apply to solvingcertain or some nonlinear models.We need new ways to get the exact solutions to nonlinearmodels with some practical backgrounds in mechanics and biology.This thesis aims at studying nonlinear models with some practical backgrounds inmechanics and biology and tries to get the exact traveling wave solutions toDodd-bullough-Mikhailov model,Landou-Ginburg-Higgss model and a series of NonlinearEvolutional Models by means of complete discriminaton system of polynomial proposed byLiu Chengshi. In the process of solving the generalized or high order equation, we can seethat the method of complete discriminaton system of polynomial is better than other methods.At the same time, the thesis gets the exact solutions to Buegers-huxley model and thenonlinear hyperbolic variational model by means of Liu's proposed trial equation method.Compares with other existing method, trial equation method is established in the deepermathematical principles, that is, it establishes nonlinear model according to practicalproblems and factorizes nonlinear ordinary differential operators. Even if the equation itselfcan not be accumulated, but an integrable equation can be divided from the model, thusgetting part of its exact solution, which is a big change in the concept of solving.