CAJ | 학술논문

研究了一个非线性浅水波动方程的孤立子解，运用微分方程定性理论，证明了向左迁移的暗孤子解的存在性，并分析了暗孤子解的一些定性特征：该解具有对称性，其振幅随着波速的增大而增加，不同波速的暗孤子解必相交于对称的两点，在无穷远处呈指数衰减到零。
연구료일개비선성천수파동방정적고립자해，운용미분방정정성이론，증명료향좌천이적암고자해적존재성，병분석료암고자해적일사정성특정：해해구유대칭성，기진폭수착파속적증대이증가，불동파속적암고자해필상교우대칭적량점，재무궁원처정지수쇠감도령。
This paper studied the soliton solutions of a nonlinear shallow water wave equation. By using the qualitative theorem of differential equations we prove the existence of dark soliton solutions and discussed some of their qualitative characteristics. The dark soliton solutions are symmetric on both sides of the crest and the amplitude increases with the increase of wave speed. Dark soliton solutions of different speeds intersect each other in two symmetrical spots and decay exponentially to zero in infinity.