Restructuring Coupled Nonlinear Klein-Gordon Equations to Advection-Coupled Systems for Oceanographic Applications
Abstract
This study presents the mathematical restructuring of coupled nonlinear Klein-Gordon equations to incorporate advection terms for oceanographic wave modeling applications. The classical Klein-Gordon system, while effective for various wave phenomena, lacks explicit consideration of advective transport crucial in ocean wave-current interactions. We systematically introduce an advection term ku_x to the standard coupled Klein-Gordon framework, transforming it into an advection-coupled system suitable for shallow water wave dynamics. The restructured system consists of the equations u_{xx} - u_{tt} - u + ku_x + 2u³ + 2uv = 0 and v_x - v_t - 4uu_t = 0, where u represents wave displacement, v represents particle velocity, and k is the advection parameter characterizing background current strength. Mathematical analysis reveals that the advection parameter fundamentally alters the system's symmetry structure, breaking space-time invariance and introducing directional preference reflecting physical reality of background flow. The restructured equations provide enhanced capability for modeling wave propagation in environments with significant current interactions, offering improved theoretical foundation for coastal engineering applications, pollutant transport modeling, and marine structure design.
Keywords
Klein-Gordon equations, advection coupling, oceanographic modeling, wave-current interactions
Citations
IRE Journals:
Boaz Barasa Masinde , Vincent Marani , Michael Oduor Okoya
"Restructuring Coupled Nonlinear Klein-Gordon Equations to Advection-Coupled Systems for Oceanographic Applications" Iconic Research And Engineering Journals Volume 9 Issue 2 2025 Page 1108-1113
IEEE:
Boaz Barasa Masinde , Vincent Marani , Michael Oduor Okoya
"Restructuring Coupled Nonlinear Klein-Gordon Equations to Advection-Coupled Systems for Oceanographic Applications" Iconic Research And Engineering Journals, 9(2)
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