# Advanced Mathematical Physics Problems

**Type:** Topics  
**Canonical URL:** https://scholariq.org/topics/advanced-mathematical-physics-problems/

## Facts

| Field | Value |
| --- | --- |
| Description | This cluster of papers focuses on the global well-posedness, scattering, and blow-up phenomena for various nonlinear wave equations, including the nonlinear Schrödinger equation, wave maps equation, Korteweg-de Vries equation, and dispersive equations. The research also explores the behavior of solitons and critical exponent for energy-critical equations. |
| Domain | Physical Sciences |
| Field | Mathematics |
| OpenAlex ID | t11654 |
| Works | 10 |

## Topic papers all

- [Localized states in discrete nonlinear Schrödinger equations](https://scholariq.org/papers/localized-states-in-discrete-nonlinear-schrodinger-equations/)
- [Spatiotemporal deformation of lump solution to (2+1)-dimensional KdV equation](https://scholariq.org/papers/spatiotemporal-deformation-of-lump-solution-to-2-1-dimensional-kdv-equation/)
- [Infinitely many solutions for a gauged nonlinear Schrödinger equation](https://scholariq.org/papers/infinitely-many-solutions-for-a-gauged-nonlinear-schrodinger-equation/)
- [Exact travelling wave solutionsof some nonlinear evolutionary equations](https://scholariq.org/papers/exact-travelling-wave-solutionsof-some-nonlinear-evolutionary-equations/)
- [Local 4/5-law and energy dissipation anomaly in turbulence of incompressible MHD Equations](https://scholariq.org/papers/local-4-5-law-and-energy-dissipation-anomaly-in-turbulence-of-incompressible-mhd/)
- [Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-nonlinear-schrodinger/)
- [Random data final-state problem of fourth-order inhomogeneous NLS](https://scholariq.org/papers/random-data-final-state-problem-of-fourth-order-inhomogeneous-nls/)
- [Almost sure scattering for defocusing energy critical Hartree equation on $\R^5$](https://scholariq.org/papers/almost-sure-scattering-for-defocusing-energy-critical-hartree-equation-on-r-5/)
- [Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-hartree-nonlinear-wave/)
- [Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-hartree-nonlinear-wave-2/)

## Topic primary papers

- [Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-nonlinear-schrodinger/)
- [Random data final-state problem of fourth-order inhomogeneous NLS](https://scholariq.org/papers/random-data-final-state-problem-of-fourth-order-inhomogeneous-nls/)
- [Almost sure scattering for defocusing energy critical Hartree equation on $\R^5$](https://scholariq.org/papers/almost-sure-scattering-for-defocusing-energy-critical-hartree-equation-on-r-5/)
- [Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-hartree-nonlinear-wave/)
- [Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation](https://scholariq.org/papers/global-well-posedness-of-the-energy-critical-stochastic-hartree-nonlinear-wave-2/)

---
Source: ScholarIQ — public research metadata, principally OpenAlex. See https://scholariq.org/sources/ for provenance and https://scholariq.org/methodology/ for what these figures mean.