Quantum mechanics

Chaotic

Mathematical physics

Statistics

Atomic physics

Superposition principle

Computer science

Physics

Mathematics

Exponential decay

Resonance (particle physics)

Exponential function

Bilinear interpolation

Mathematical analysis

Artificial intelligence

Applied Mathematics Letters

Resonance phenomena occur widely in fluid, physics and other fields, e.g., they are related with the optical elements, the well-balanced scheme for shallow water with discontinuous topography, and some phenomena in chaotic dynamics and fluid dynamics. Application of the principle of linear superposition to the Hirota bilinear equation gives rise to a sufficient and necessary condition for the existence of multi-exponential wave solutions. We study the resonance behavior based on the construction of multi-exponential wave solution to two extended (3 + 1)- dimensional Jimbo–Miwa equations. The resonance characteristics are analyzed and simulated for some resonant two-wave and three-wave solutions.

Multi-exponential wave solutions to two extended Jimbo–Miwa equations and the resonance behavior