Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

Abstract

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.

12 pages

References in corpus (4)

• The general solution of the matrix equation $w_t+\sum _{k=1}^n{w}_{x_k}{\rho }^{(k)}(w)=\rho (w)+[w,T\tilde{\rho }(w)]$
• Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions
• Partially integrable systems in multidimensions by a variant of the dressing method. 1
• Matrix equations of hydrodynamic type as lower-dimensional reductions of Self-dual type $S$-integrable systems

Cited by in corpus (1)

• On the remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf-Cole transformation