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We perform numerical simulations using immersed boundary methods for flow over fish, single and in tandem arrangements, performing traveling wave like motion. We analyze nonlinear mechanics of hydrodynamic lateral side-force and drag/thrust coefficients. We compute their Fourier spectra and find that lateral side force carries fundamental and odd harmonics while drag is composed of even harmonics when single fish swim in free-stream. For tandem arrangement, we set the phase-speed of downstream fish as 0.75 times that of upstream fish. Fourier spectra of lateral force for both upstream and downstream fish are composed of forcing frequencies of both the fish. Even harmonics of forcing frequencies along with combined modes at sum and difference of these frequencies appear in their drag-spectra. We also investigate the symmetric or antisymmetric nature of the fundamental and combined modes using the conventional symmetry principles and proper orthogonal decomposition technique. We show that the results obtained from both of these techniques agree well with each other. However, we also find some anomalies in case of fish swimming in tandem configuration. [ABSTRACT FROM AUTHOR]