To impart knowledge to Sanakadi Rishis and Lord Brahma, Lord Vishnu incarnated as the divine Hamsa, also known as Mahahamsa. The dialogue between the Sanakadi Rishis and Lord Hamsa is recorded in Hamsa Gita. Lord Hamsa is the embodiment of metaphysical wisdom. He provides guidance to the seekers of spiritual liberation or Moksha.
The description of Lord Vishnu's Hamsa Avatara is found in Srimad Bhagavata Mahapurana, Mahabharata, Uddhava Gita and Shri Vishnu Sahasranama. Lord Vishnu, in His Hamsavatara imparts metaphysical knowledge concerning the subconscious mind, intellect, transient mind, ego and the senses to the world through His dialogue with Sanakadi Rishis.
Once, Lord Brahma was presiding over His divine council. At that time, Sanakadi Rishis arrived there. The Sanakadi Rishis constantly engaged in spiritual discourse about Lord Vishnu. Thus, they began discussing the subject of Moksha with Lord Brahma. The Sanakadi Rishis thus posed their question to Lord Brahma and asked - "Father! The subconscious mind perpetually contemplates sensory pleasure and Gunas, and the worldly desires become a constant force to engage this mind. Thus, the subconscious mind and the Gunas become deeply interwoven. In such a state, when a person wishes to attain Moksha from this ocean of great sufferings, how should they learn to discriminate the subconscious mind from Guna and worldly desires."
As Lord Brahma was engaged with the task of the creation of the universe, He couldn't comprehend the core essence and philosophical complexity of the question posed by the Sanakadi Rishis. Thus, He invoked Lord Vishnu. In response to Lord Brahma's invocation, Lord Vishnu manifested Himself to bestow upon Sanakadi Rishis, as well as the entire humanity through them, the profound knowledge for the attainment of Moksha. He incarnated as Mahahamsa, emanating a divine golden aura, and dispelled the doubts of Sanakadi Rishis.
Lord Hamsa says - "The entire body, along with the life force and the senses, is governed by Prarabdha Karma. Therefore, the body exists as long as the Prarabdha Karma last. But, a person who attains enlightenment through self-realization learns to distinguish between the physical body and the conscious self. O Sages! This is the core philosophy of Samkhya Darshan and Yoga Marga. I have transcended the physical attributes of being, and thus I am the benefactor, well-wisher, beloved and the soul pervading through the entire humanity. Thus, it is me who alone witness the three states of existence - the waking state, the dreaming state and the state of deep sleep. If a person constantly contemplates worldly desires, then his subconscious mind becomes entrenched in worldly desires, and the person who constantly meditates on my name attains spiritual oneness with me."
Thus, after receiving the profound wisdom from Lord Hamsa, everyone worshipped Lord Hamsa and sang hymns in His praise. Thereafter, the Mahahamsa Avatara of Lord Vishnu disappeared and returned to His divine abode.
Hamsa Avatara is the self-manifested incarnation of Lord Vishnu, thus no description of His parentage, consort, etc, is found in religious texts.
In Hamsa Avatara, Lord Vishnu is depicted as a divine swan. Lord Hamsa is also portrayed as a great swan imparting knowledge to Sanakadi Rishis. In Mahabharata, Lord Hamsa is depicted as a Swan radiant with golden aura.
Lord Hamsa Vedic Mantra -
हकारेण बहिर्याति सकारेण विशेत्पुनः।
हंसहंसेत्यमुं मन्त्रं जीवो जपति सर्वदा॥
Hakarena Bahiryati Sakarena Vishetpunah।
Hamsahamsetyamum Mantram Jivo Japati Sarvada॥
Shri Hamsa Gayatri Mantra -
ॐ परमहंसाय विद्महे महातत्त्वाय धीमहि।
तन्नो हंस: प्रचोदयात्॥
Om Paramahamsaya Vidmahe Mahatattvaya Dhimahi।
Tanno Hamsah Prachodayat॥
Lord Hamsa Pauranika Mantra -
प्राणिनां देहमध्ये तु स्थितो हंसः सदाऽच्युतः।
हंस एव परं सत्यं हंस एव तु शक्तिकम्॥
हंस एव परं वाक्यं हंस एव तु वैदिकम्।
हंस एव परो रुद्रो हंस एव परात्परम्॥
Praninam Dehamadhye Tu Sthito Hamsah Sadachyutah।
Hamsa Eva Param Satyam Hamsa Eva Tu Shaktikam॥
Hamsa Eva Param Vakyam Hamsa Eva Tu Vaidikam।
Hamsa Eva Paro Rudro Hamsa Eva Paratparam॥