The Interaction Solutions Of Several Nonlinear Wave Equations

Nonlinear evolution equations are widely applied in physics,chemistry,fluid mechanics,oceanography,ecology,medicine and biology,and so on.In particular,it is quite significant to study the nonlinear wave equations.At present,a plenty of methods have been put forward to study their exact solutions,such as scattering transformation,B?cklund transformation,Hirota bilinear method,sine-cosine method,exponential function method,homogeneous balance method,auxiliary constant differential equation method,separation of variables method,trigonometric series method,heuristic function method,superposition method,hyperbolic tangent function method,continuation F-expansion method,classical and non-classical Lie group method,continuation Tanh function method,(G ’/ G)expansion method and,direct reduction method,and functional separation of variables,and so on.People use these methods to solve nonlinear wave equations,and gain a lot of practical solutions.At the same time,some new solutions also reveal complex physical phenomena.The proposal of these methods broadens the research scope of the nonlinear wave equations.In the dissertation,we firstly investigate the CRE solvability of the(2+1)-dimensional Konopelchenko-Dubrovsky equation under two different assumptions,namely the positive exponential polynomial hypothesis and the negative exponential polynomial assumption.Combining the Jacobi elliptic function with the third type of incomplete elliptic integral,we figure out twenty interacting solutions: the interaction solution of the torsion type,the interaction solution of the periodic type,the interaction solution of the sharp wave type and so on,draw and conclude the analysis of the corresponding waveform diagram.Secondly,a class of(2+1)-dimensional breaking soliton(BS)equation is investigated.The CRE under the assumption of positive exponential polynomial is solvable.We gain three interacting solutions by combining the Jacobi elliptic function and the third type of incomplete elliptic integral,draw and conclude the analysis of the corresponding waveform diagram.Then,the CRE solvability of the Boussinesq-Burgers equation under positive exponential polynomial assumption is investigated.Six interaction solutions are obtained by combining the Jacobi elliptic function and the third type of incomplete elliptic integral.Figures are drawn and the conclusion analysis of the corresponding waveform diagram are given.Finally,we summarize the work of this dissertation,and propose prospect for the unsolved problems.