New Trends in Nonlinear Waves

Dear Colleagues,

The Special Issue of this scientific journal delves into the forefront of mathematical research, concentrating on nonlinear waves and evolution partial differential equations. Embracing cutting-edge concepts, it specifically spotlights six critical aspects: well-posedness, blow-up phenomena, scattering phenomena, stability/instability, and variational and geometrical approaches to studying PDEs. The intricate behavior of nonlinear waves and their interactions constitutes a fundamental topic worthy of exploration within this Special Issue. Articles may analyze the long-time behavior phenomena, investigating how waves evolve and disperse over time. The quest for stability within evolving systems takes center stage. The Special Issue probes deep into the concepts of stability/instability and scattering, inspecting how solutions of nonlinear wave equations behave over extended periods and different geometric frameworks. This examination not only refines theoretical frameworks but also unveils the stability constraints crucial for real-world applications. Addressing the foundational aspect of well-posedness, the Special Issue explores new formulation and solution behaviors of nonlinear evolution PDEs. Articles aim to establish robust frameworks that ensure the existence, uniqueness, and stability of solutions, providing a critical foundation for advancing mathematical models in diverse domains. Furthermore, variational and geometric approaches to solving nonlinear PDEs have emerged as highly significant, and this Special Issue aims to showcase its efficacy in providing elegant solutions and exploring the behavior of nonlinear systems settled on general ambient spaces.

Dr. Mirko Tarulli
Guest Editor

Manuscript Submission Information

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• Scrödinger-type equations
• wave-type equations
• well-posedness
• blow-up
• scattering
• stability
• concentration–compactness
• Hamiltonian systems
• nonlinear PDEs
• geometry