TY - JOUR

T1 - Properties of the Magma and Modified Magma Equations

AU - Takahashi, Daisuke

AU - Satsuma, Junkichi

AU - Sachs, Jeffrey R.

PY - 1990

Y1 - 1990

N2 - Solutions of the “magma equation”, ft=[fn{(f-mft)x-1}]x, are investigated for compact support initial conditions. It is shown analytically that traveling wave solutions with compact support do not exist for this equation. Numerical integration demonstrates that although initial conditions with compact support produce solitary waves, these solitary waves do not interact like solitons. Moreover, a relationship between the magma equation and the KdV equation is established, and this relationship is used to explain previously observed soliton-like behavior. Both equations are shown to be related to the modified magma equation, FT+[F3(3FXX+1)]x=0, which is proven to have N-soliton solutions with compact support and an infinite number of conserved densities.

AB - Solutions of the “magma equation”, ft=[fn{(f-mft)x-1}]x, are investigated for compact support initial conditions. It is shown analytically that traveling wave solutions with compact support do not exist for this equation. Numerical integration demonstrates that although initial conditions with compact support produce solitary waves, these solitary waves do not interact like solitons. Moreover, a relationship between the magma equation and the KdV equation is established, and this relationship is used to explain previously observed soliton-like behavior. Both equations are shown to be related to the modified magma equation, FT+[F3(3FXX+1)]x=0, which is proven to have N-soliton solutions with compact support and an infinite number of conserved densities.

KW - KdV equation

KW - compact support solution

KW - integrable

KW - magma equation

KW - soliton

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U2 - 10.1143/JPSJ.59.1941

DO - 10.1143/JPSJ.59.1941

M3 - Article

AN - SCOPUS:0039066125

SN - 0031-9015

VL - 59

SP - 1941

EP - 1953

JO - journal of the physical society of japan

JF - journal of the physical society of japan

IS - 6

ER -