## Quasi-classical asymptotics of solutions to the matrix factorization problem with quadratically oscillating off-diagonal elements.(English. Russian original)Zbl 1307.35179

Funct. Anal. Appl. 48, No. 1, 1-14 (2014); translation from Funkts. Anal. Prilozh. 48, No. 1, 1-18 (2014).
The paper investigates the asymptotic behavior of solutions of the $$2\times 2$$ matrix Riemann-Hilbert problem $$H^+=H^- V$$ on the real axis where the matrix $$V(x)$$ has the off-diagonal elements $$b(x)e^{-itx^2/2}$$ and $$c(x)e^{itx^2/2}$$. The matrix $$V(x)$$ becomes the identity matrix as $$x \to \infty$$. The authors prove that the factorization problem has a solution at sufficiently large $$t$$. The asymptotics of this solution is described by an expansion in the power-logarithmic series in $$t$$.

### MSC:

 35Q15 Riemann-Hilbert problems in context of PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 35B40 Asymptotic behavior of solutions to PDEs
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### References:

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