TY - JOUR
T1 - Undular bores in the (3+1) dimensional mKP equation
AU - Ozdemir, Nese
AU - Demirci, Ali
AU - Ahmetolan, Semra
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/9/28
Y1 - 2023/9/28
N2 - Undular bore (dispersive shock wave) solutions in the (3+1) dimensional modified Kadomtsev-Petviashvili (mKP) equation for step type initial condition along a paraboloid type wavefront are found. Then, using a suitable solution form for the (3+1) dimensional mKP equation, it is reduced to the (1+1) dimensional focusing spherical mKdV (smKdV) and defocusing spherical mKdV (smKdV(d)) equations. Next, the Whitham modulation equations of the smKdV and smKdV(d) equations are found in terms of Riemann variables. Numerical solutions of the derived modulation equations are obtained. Also, an error analysis is performed for direct numerical solutions of both smKdV and smKdV(d).
AB - Undular bore (dispersive shock wave) solutions in the (3+1) dimensional modified Kadomtsev-Petviashvili (mKP) equation for step type initial condition along a paraboloid type wavefront are found. Then, using a suitable solution form for the (3+1) dimensional mKP equation, it is reduced to the (1+1) dimensional focusing spherical mKdV (smKdV) and defocusing spherical mKdV (smKdV(d)) equations. Next, the Whitham modulation equations of the smKdV and smKdV(d) equations are found in terms of Riemann variables. Numerical solutions of the derived modulation equations are obtained. Also, an error analysis is performed for direct numerical solutions of both smKdV and smKdV(d).
KW - Spherical reductions
KW - Undular bore solution
KW - Whitham modulation theory
UR - http://www.scopus.com/inward/record.url?scp=85167789000&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2023.129051
DO - 10.1016/j.physleta.2023.129051
M3 - Article
AN - SCOPUS:85167789000
SN - 0375-9601
VL - 483
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
M1 - 129051
ER -