| Nonlinear evolution equations can describe nonlinear phenomenas in many fields,and have been widely used in fluids,plasmas and other fields.The analytical solutions of nonlinear evolution equations can provide more physical information and more understanding of physical characteristics,and play an important role in nonlinear physics.This article mainly studies three nonlinear evolution equations in plasmas and other fields based on symbolic computation.The main work is summarized as follows:The properties of solitons,breathers and lumps of the(3+1)-dimensional generalized Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation in fluids are studied.The effects of the coefficients in the equation on solitons,breathers and lumps are also discussed.The changes in coefficient affect the positions of solitons,breathers and lumps.The amplitudes of solitons is not affected by the change in coefficient,but the amplitudes of breathers and lumps change with the change in coefficient.The analytical solutions of the generalized(3+1)-dimensional Wazwaz equation in ocean physics are studied.The propagation properties of solitons and breathers are analyzed through images.The shape and amplitude of one soliton and first-order breather remain unchanged during the propagation process.The interactions between two solitons,second-order breathers and first order breather and one soliton are elastic.The position of one and two solitons is affected by all the coefficients in the equation.The propagation direction of one and two solitons is related to the coefficient c,and the propagation direction of two solitons is also related to the coefficient 7.The generalized(3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in plasmas is studied.Using Hirota method,the bilinear forms,one-and two-soliton solutions are obtained.The propagation characteristics of one soliton and interactions between two solitons are analyzed using images.Over time,one soliton maintain its original direction,amplitude and velocity.The interaction between X type two solitons is elastic,while Y type two solitons is inelastic.Before the interaction,the parallel type two solitons move in opposite directions to each other,merge into one wave at the moment of the interaction,and then resplit into two waves that propagate in their original direction after the interaction,while maintaining the original amplitude and velocity.The coefficients b and d in the equation affect the propagation direction and velocity of parallel type two solitons. |
