Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation

Wang, Shu; Wang, Huifeng

doi:10.3390/axioms15030230

Open AccessArticle

Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation

by

Shu Wang

and

Huifeng Wang

^*

School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100021, China

^*

Author to whom correspondence should be addressed.

Axioms 2026, 15(3), 230; https://doi.org/10.3390/axioms15030230

Submission received: 15 February 2026 / Revised: 7 March 2026 / Accepted: 16 March 2026 / Published: 20 March 2026

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Abstract

In this work, we address the nonhomogeneous initial-boundary value problem for the coupled Hirota equation posed on the finite interval

[0, L]

. To investigate the well-posedness of this problem, we first adopt an appropriate transformation, namely the Laplace transform, which is tailored to the specific characteristics of the problem, and further obtain an explicit solution formula for the linear inhomogeneous coupled system. Subsequently, the local well-posedness of the original nonhomogeneous initial-boundary value problem in

X_{s, T} \times X_{s, T} (X_{s, T} = C (0, T; H^{s} (0, 1)) \cap L^{2} (0, T; H^{s + 1} (0, 1)))

is rigorously established through the combination of this explicit formula, the contraction mapping principle and energy estimates.

Keywords: coupled Hirota equation; nonhomogeneous boundary value problem; local well-posedness

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MDPI and ACS Style

Wang, S.; Wang, H. Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation. Axioms 2026, 15, 230. https://doi.org/10.3390/axioms15030230

AMA Style

Wang S, Wang H. Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation. Axioms. 2026; 15(3):230. https://doi.org/10.3390/axioms15030230

Chicago/Turabian Style

Wang, Shu, and Huifeng Wang. 2026. "Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation" Axioms 15, no. 3: 230. https://doi.org/10.3390/axioms15030230

APA Style

Wang, S., & Wang, H. (2026). Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation. Axioms, 15(3), 230. https://doi.org/10.3390/axioms15030230

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Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation

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