CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System

Abstract

The consistent tanh expansion (CTE) method is successfully applied to the coupled integrable dispersionless (CID) system. A nonauto-Bäcklund transformation (BT) theorem includes two fields $f$ and $v_1$ is obtained by using the CTE method. One obtains the consistent condition in the nonauto-BT theorem by means of the relation between the fields $f$ and $v_1$ . The CID system possesses the CTE solvability property by some detailed analysis. Many interactions between one soliton and multiple resonant solitons, and between one soliton and cnoidal waves are generated by using the nonauto-BT theorem. The types of bright and gray two front waves are shown by some figures. In the meanwhile, the nonlocal symmetry is obtained by the truncated Painlevé method and the Möbious invariant form. The initial value problem and an auto-BT are constructed by the localization procedure.