Unconditional local and global well-posedness proved for the two-parameter MMT equation on the torus in Sobolev spaces, with flow map shown not C^3 at origin for positive derivative order.
Unconditional uniqueness of solutions for nonlinear dispersive equations
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Establishes local well-posedness in H^s(T) for s ≥ 1/2 and global well-posedness under small L^2 norm for periodic INLS using gauge transform and CCM integrability, plus unconditional energy-space results and infinite-depth convergence.
Sharp local well-posedness holds for the Hirota-Satsuma system in H^k(R) × H^s(R) with k and s possibly unequal, determined by the dispersion ratio, generalizing the equal-regularity case.
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Unconditional Well-posedness for the MMT Equation on the Torus
Unconditional local and global well-posedness proved for the two-parameter MMT equation on the torus in Sobolev spaces, with flow map shown not C^3 at origin for positive derivative order.
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Well-posedness for the periodic Intermediate nonlinear Schr\"{o}dinger equation
Establishes local well-posedness in H^s(T) for s ≥ 1/2 and global well-posedness under small L^2 norm for periodic INLS using gauge transform and CCM integrability, plus unconditional energy-space results and infinite-depth convergence.
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Sharp local well-posedness for the Hirota-Satsuma system
Sharp local well-posedness holds for the Hirota-Satsuma system in H^k(R) × H^s(R) with k and s possibly unequal, determined by the dispersion ratio, generalizing the equal-regularity case.