In this paper, some novel lump solutions and interaction phenomenon between lump and kink M-soliton are investigated. Firstly, we study the evolution and degeneration behaviour of kink breather wave solution with difffferent forms for the (3+1)-dimensional Hirota-Satsuma-Ito-like equation by symbolic computation and Hirota bilinear form. In the process of degeneration of breather waves, some novel lump solutions are derived by the limit method. In addition, M-fifissionable soliton and the interaction phenomenon between lump solutions and kink M-solitons (lump-M-solitons) are investigated, the theorem and corollary about the conditions for the existence of the interaction phenomenon are given and proved further. The lump-M-solitons with difffferent types is studied to illustrate the correctness and availability of the given theorem and corollary, such as lump-cos type, lump-cosh-exponential type, lump cosh-cos-cosh type. Several three-dimensional fifigures are drawn to better depict the nonlinear dynamic behaviours including the oscillation of breather wave, the emergence of lump, the evolution behaviour of fission and fusion of lump-M-solitons and so on.

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Exact homoclinic breather wave solution for the coupled Schrödinger-Boussinesq equation is obtained by using homoclinic test technique. Based on the homoclinic breather wave solution, rational homoclinic breather wave solution is generated by homoclinic breather limit method, rogue wave in the form of the rational homoclinic solution is derived when the period of homoclinic breather wave goes to infinite. This is a new way for generating rogue wave which is different from direct constructing method, Darboux dressing technique and ansätz with complexity of parameter. This result shows the homoclinic rogue wave can be generated from homoclinic breather wave, and it is useful for explaining some related nonlinear phenomenon.