Research On Analytical Solutions Of Nonlinear Evolution Equations In Physical Fields Such As Fluids

Nonlinear evolution equations have been used as the models to de-scribe nonlinear phenomena in physical fields such as fluids.By studying the characteristics of the solutions of the nonlinear evolution equations,some theoretical support can be provided for some physical experiments.In the paper,three nonlinear evolution equations in the fields of physics such as fluids are studied analytically.The main work of this paper is summarized as follows:Via the Hirota method and symbolic computation,we obtain the lump,mixed lump-stripe,mixed rogue wave-stripe and breather wave so-lutions of a(3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation.We graphically show the interactions between a rogue wave and a pair of stripe waves,and between a lump and a stripe wave.Besides,the breather wave propagates steadily in a certain direction.By virtue of the homoclinic-test,ansatz and polynomial-expansion methods,we construct the breather and lump solutions,shock wave so-lutions and travelling-wave solutions of a(3+1)-dimensional generalized Kadomtsev-Petviashvili equation,respectively.We graphically analyze the propagation characteristics of these solutions and the effect of the coefficients in the equation on the breather wave,lump wave and shock wave.Via the Hirota method and Hirota-Riemann function method,the bilinear form,Backlund transformation,soliton solutions and periodic wave solutions of the Calogero-Bogoyavlenskii-Konopelchenko-Schiff are obtained.By the calculations,we find that the coefficients in the equa-tion affect the velocities of the one/two solitons,but not their amplitudes or directions of the propagations.We graphically demonstrate that the interaction between two solitons is elastic.We analyse the asymptotic properties of one-periodic wave solutions which reveal the connection be-tween the one-periodic wave solutions and the one-soliton solutions,i.e.,the one-periodic wave solutions tend to the one-soliton solutions under the limit process.