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- W2032651925 abstract "Abstract We consider the class of non-integrable, non-linear equations, L q K=K 2 , L q =⊸ + ∑ 1⩽i+j⩽q aij∂ i x i ∂ j t j , ⊸≠0, in 1+1 dimensions. We seek rational solutions K(ω1,ω2), which we call bi-solitons, with exponential type variables ωi = exp(γix + ρit). In this paper, we restrict to q = 2 and 3, and investigate the general q case in the following paper. We find that these bi-solitons exist when the operator Lq (with ± ϵ) can be factorized as the product of smaller order differential operators. Besides the trivial factorized bi-solitons, we show that there exist non-trivial ones whenever K may be written as Σlmaxx ωl2Fl(Z = ω1 + ω2). In order to understand the origin of the factorization property, to any polynomial K = Σωl2Fl(Z) we associate a linear transformation such that LqK has only the power ωl2 of K2. For q = 2 and 3, we find that there exist particular polynomials of this type restraining Lq to be a product of smallr order operators. For the full non-linear equations we verify that all the bi-solitons can be obtained from these particular polynomials." @default.
- W2032651925 created "2016-06-24" @default.
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- W2032651925 date "1982-10-01" @default.
- W2032651925 modified "2023-10-18" @default.
- W2032651925 title "Bi-solitons for a class of non-linear equations with quadratic non-linearity. II" @default.
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- W2032651925 doi "https://doi.org/10.1016/0167-2789(82)90003-3" @default.
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