Solitons and symmetry reduction solutions of a nonlocal two‐mode Korteweg–de Vries equation

摘要

The two‐mode Korteweg–de Vries (TMKdV) equation describes propagation of two different waves modes simultaneously. By using consistent correlated bang (CCB) method, a nonlocal form of the TMKdV equation is constructed and converted into two local equations with its dependent variables having definite parity. Multiple soliton solutions of the nonlocal TMKdV equation are obtained by using known multiple soliton solutions of the TMKdV equation, and some singular travelling wave solutions are also generated in a similar way. The classical Lie symmetry method is also carried on the nonlocal TMKdV equation to get its symmetry reduction solutions.