Abstract
AbstractIn the context of the initial data and an amplitude parameter $$\varepsilon $$
ε
, we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space $$H^k$$
H
k
as long as $$k>5/2$$
k
>
5
/
2
. Additionally, we illustrate that the threshold time for the occurrence of wave breaking in the surging type is on the order of $$\varepsilon ^{-1},$$
ε
-
1
,
while plunging breakers do not manifest. Lastly, in accordance with ODE theory, it is demonstrated that there are no exact solitary wave solutions in the form of sech and $$sech^2$$
s
e
c
h
2
.
Publisher
Springer Science and Business Media LLC
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