Geodesic
Three-wave resonance in the two-dimensional stationary problem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 63-67

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In the theory of two-dimensional stationary gas dynamics, the potential isentropic motion of a perfect ideal gas on the constant homogeneous supersonic background is considered. The problem on the interaction of three traveling waves with slowly varying amplitudes and phases along the direction of the background flow is solved in the case when the sum of “harmonic” phases is exactly equal to zero. The equations of amplitude and phase variations of the waves are derived, an analytical study of their solutions is conducted. The question of what the boundary conditions should be satisfied is discussed. 
@article{VMUMM_2019_2_a13,
     author = {A. N. Golubyatnikov and D. V. Ukrainskii},
     title = {Three-wave resonance in the two-dimensional stationary problem},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {63--67},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a13/}
}
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A. N. Golubyatnikov; D. V. Ukrainskii. Three-wave resonance in the two-dimensional stationary problem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 63-67. http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a13/