The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech$$^2$$ solutions
The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech$$^2$$ solutions
Abstract In the context of the initial data and an amplitude parameter $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> , we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space $$H^k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>k</mml:mi> </mml:msup> </mml:math> …