New stationary vortex solutions of the Hasegawa–Mima equation

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Abstract
Two different families of explicit stationary solutions of the Hasegawa–Mima equation are obtained. In the first case the well-known modon (dipole vortex) is used as the zeroth-order solution, and new solutions that are close to but distinctly different from it are found by perturbation analysis. In the second case the dispersive term of the equation is treated as a small parameter, and a radially symmetric solution (a monopole vortex) is used as the zeroth-order approximation. Both families of solutions are found to be infinite and to contain an arbitrary function. A recent general proof of the existence of infinitely many stationary solutions containing an arbitrary function is examined and found to be invalid.