About linear superpositions of special exact solutions of Veselov-Novikov equation

Details About linear superpositions of special exact solutions of Veselov-Novikov equation About linear superpositions of special exact solutions of Veselov-Novikov equation

2011-10-07

arxiv.org/abs/1110.1626v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of linear superpositions of arbitrary number of exact special solutions $u^{(n)}$, $n=1,...,N$ are constructed via $\bar\partial$-dressing method in such a way that the sums $u= u^{(k_1)}+...+ u^{(k_m)}$, $1\leqslant k_1

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