Breathers and rogue waves for semilinear curl-curl wave equations
Breathers and rogue waves for semilinear curl-curl wave equations
Abstract We consider localized solutions of variants of the semilinear curl-curl wave equation $$s(x) \partial _t^2 U +\nabla \times \nabla \times U + q(x) U \pm V(x) \vert U \vert ^{p-1} U = 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mi>U</mml:mi> <mml:mo>+</mml:mo> …