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- W3021314861 abstract "We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching different plane waves $$A_jmathrm {e}^{mathrm {i}phi _j}mathrm {e}^{-2mathrm {i}B_jx}$$ , $$j=1,2$$ as $$xrightarrow pm infty $$ . The goal is to determine the long-time asymptotics of the solution, according to the value of $$xi =x/t$$ . The general situation is analyzed in a recent paper where we develop the Riemann–Hilbert approach and detect different asymptotic scenarios, depending on the relationships between the parameters $$A_1$$ , $$A_2$$ , $$B_1$$ , and $$B_2$$ . In particular, in the shock case $$B_1<B_2$$ , some scenarios include genus 3 sectors, i.e., ranges of values of $$xi $$ where the leading term of the asymptotics is given in terms of hyperelliptic functions attached to a Riemann surface $$M(xi )$$ of genus three. The present paper is devoted to the complete asymptotic analysis in such a sector." @default.
- W3021314861 created "2020-05-13" @default.
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- W3021314861 date "2022-01-28" @default.
- W3021314861 modified "2023-09-30" @default.
- W3021314861 title "The Focusing NLS Equation with Step-Like Oscillating Background: The Genus 3 Sector" @default.
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- W3021314861 doi "https://doi.org/10.1007/s00220-021-04288-4" @default.
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