TITLE:
Existence of Solutions for Shallow Water Equatorial Waves
AUTHORS:
Ranis Nail Ibragimov, Svetlin Georgiev, Deliang Bao, Joy Williams
KEYWORDS:
Shallow Water, Equatorial Waves, Existence of Solutions, Integral Presentation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.2,
February
10,
2026
ABSTRACT: The study focuses on the modeling of nonlinear shallow water equatorial free boundary waves. It has been demonstrated that there exists at least one solution, at least two nonnegative solutions, and at least three nonnegative solutions within the time scales considered. To achieve this, the original nonlinear model is transformed into a linear system using the hodograph method. Subsequently, the mapped system is represented through a new integral formulation that involves two operators. These operators are designed to ensure that any fixed point of their sum corresponds to a solution of the problem at hand.