Classification of soliton solutions of the modified Boussinesq equation
Chen Liu, Chuanzhong Li
Source abstract
A classification of soliton solutions is established for the modified Boussinesq (mBoussinesq) equation, which arises from the 3-reduction of the modified Kadomtsev-Petviashvili hierarchy. We prove that when all κ-parameters are nonzero, the soliton solutions can be expressed in terms of τ-functions associated with a single Grassmannian. When a zero κ-parameter is present, certain table solitons degenerate into kink solitons, and the solutions are described by τ-functions associated with two Grassmannians of different dimensions. On this basis, we present specific examples and apply combinatorial tools such as chord diagrams and pipe dreams to systematically analyze the asymptotic behavior and internal structures of the soliton solutions.
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