## About this Research Topic

Partial differential equations have become a useful tool to describe the natural phenomena of science and engineering. Nonlinear evolution equations (NLEEs) arise in many branches of science such as mathematics, physics, mechanics, water waves, computational fluid dynamics, optics, quantum mechanics, shallow ...

NLEEs are widely used to describe physical phenomena in natural science, such as fluid mechanics, plasma physics, optical fibres, biology, solid-state physics, etc. Exact solutions of NLEEs play an important role in understanding the mechanisms of many physical phenomena and processes in various areas of natural science. They can help to analyze the stability of these solutions and the movement role of the wave by making graphs of the exact solutions.

Potential themes of interest in this Research Topic include, but are not limited to, the following:

• Soliton theory

• Fractional partial differential equations

• Time scale dynamic equations

• Nonlinear Rayleigh-Taylor instability

• Nonlinear Kelvin-Helmholtz instability

• Stability analysis of dynamical systems

• Nonlinear water waves

• Computational fluid dynamics

• Fiber optics

• Computational quantum mechanics

• Water waves

• Shallow water

• Nanofluids

**Keywords**:
partial differential equations, mathematical methods, dynamical system, fluid dynamics

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.