Abstract
Two types of extended KdV equations generated by squared eigenfunction symmetries are derived with Cauchy matrix approach opening up different ideas that may be of considerable interest of understanding for the integrable system’s homology. The unified-form solution is discussed through choosing different matrices of determining equation set. Furthermore, under a safe range of parameters and the integrability conditions, it is possible to construct the soliton solution into the unified form, which can also verify that Cauchy matrix approach is an effective mathematical tool for investigating the integrable system.
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