New homoclinic rogue wave solution for the coupled Schrodinger Boussinesq equation

Exact homoclinic breather wave solution for the coupled Schr¨odinger-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 ans¨atz 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.